AP Board Class 8 Maths Chapter 12 Factorisation Ex 12.2 Textbook Solutions PDF: Download Andhra Pradesh Board STD 8th Maths Chapter 12 Factorisation Ex 12.2 Book Answers |

## Andhra Pradesh Board Class 8th Maths Chapter 12 Factorisation Ex 12.2 Textbooks Solutions PDF

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Class | 8th |

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## AP Board Class 8th Maths Chapter 12 Factorisation Ex 12.2 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 8th Maths Chapter 12 Factorisation Ex 12.2 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:Question 1.

Factorise the following expression

i) a^{2} + 10a +25

ii) l^{2} – 16l + 64

iii) 36x^{2} + 96xy + 64y^{2}

iv) 25x^{2} + 9y^{2} – 30xy

v) 25m^{2}– 40mn + 1 6n^{2}

vi) 81x^{2} – 198 xy + 12ly^{2}

vii) (x+y)^{2} – 4xy

(Hint : first expand ( x + y)^{2} )

viii) l^{4} + 4l^{2}m^{2} + 4m^{4}

Solution:

i) a^{2} + 10a +25

= (a)^{2} + 2 × a × 5 + (5)^{2}

It is in the form of a^{2} + 2ab + b^{2}

a^{2} + 2ab + b^{2}= (a + b)^{2}

∴ a^{2} + 10a + 25 = (a + 5)^{2} = (a + 5) (a + 5)

ii) l^{2} – 16l + 64

l^{2} – 16l + 64

= (l)^{2} – 2 × l × 8 + (8)^{2}

It is in the form of a^{2} – 2ab + b^{2}

a^{2} – 2ab + b^{2} = (a – b)^{2}

∴ l^{2} – 16l + 64 = (l – 8)^{2} = (l – 8) (l – 8)

iii) 36x^{2} + 96xy + 64y^{2}

36x^{2} + 96xy + 64y^{2}

= (6x)^{2} + 2 × 6x × 8y + (8y)^{2}

It is in the form of a^{2} + 2ab + b^{2}

a^{2} + 2ab + b^{2} = (a + b)^{2}

∴ 36x^{2} + 96xy + 64y^{2}

= (6x + 8y)^{2} = (6x + 8y) (6x + 8y)

iv) 25x^{2} + 9y^{2} – 30xy

25x^{2} + 9y^{2} – 30xy

= (5x)^{2} + (3y)^{2} – 2 × 5x × 3y

It is in the form of a^{2} + b^{2} – 2ab

a^{2} + b^{2} – 2ab = (a – b)^{2}

∴ 25x^{2} + 9y^{2} – 30xy

= (5x – 3y)^{2} = (5x – 3y) (5x – 3y)

v) 25m^{2}– 40mn + 1 6n^{2}

25m^{2} – 40mn + 16n^{2}

= (5m)^{2} – 2 × 5m × 4n + (4n)^{2}

It is in the form of a^{2} – 2ab + b^{2}

a^{2} – 2ab + b^{2} = (a – b)^{2}

∴ 25m^{2} – 40mn + 16n^{2}

= (5m – 4n)^{2}

= (5m – 4n) (5m – 4n)

vi) 81x^{2} – 198 xy + 12ly^{2}

81x^{2} – 198xy + 121y^{2}

= (9x)^{2} – 2 × 9x × 11y + (11y)^{2}

It is in the form of a^{2} – 2ab + b^{2}

a^{2} – 2ab + b^{2} = (a – b)^{2}

∴ 81x^{2} – 198xy + 121y^{2}

= (9x – 11y)^{2} – (9x – 11y) (9x – 11y)

vii) (x+y)^{2} – 4xy

(Hint : first expand ( x + y)^{2} )

= (x + y)^{2} – 4xy

= x^{2} + y^{2} + 2xy – 4xy

= x^{2} + y^{2} – 2xy = (x – y)^{2} = (x – y)(x – y)

viii) l^{4} + 4l^{2}m^{2} + 4m^{4}

l^{4} + 4l^{2}m^{2} + 4m^{4}

= (l^{2})^{2} + 2 × l^{2} × 2m^{2} + (2m^{2})^{2}

It is in the form of a^{2} + 2ab + b^{2}

a^{2} + 2ab + b^{2} = (a – b)^{2}

∴ l^{4} + 4l^{2}m^{2} + 4m^{4}

= (l^{2} + 2m^{2})^{2} = (l^{2} + 2m^{2}) (l^{2} + 2m^{2})

Question 2.

Factorise the following

i) x^{2} – 36

ii) 49x^{2} – 25y^{2}

iii) m^{2} – 121

iv) 81 – 64x^{2}

v) x^{2}y^{2} – 64

vi) 6x^{2} – 54

vii) x^{2} – 81

viii) 2x -32 x^{5}

ix) 81x^{4} – 121x^{2}

x) (p^{2} – 2pq + q^{2})-r^{2}

xi) (x+y)^{2} – (x-y)^{2}

Solution:

i) x^{2} – 36

x^{2} – 36

⇒ (x)^{2} – (6)^{2} is in the form of a^{2} – b^{2}

a^{2} – b^{2} = (a + b) (a – b)

∴ x^{2} – 36 = (x + 6) (x – 6)

ii) 49x^{2} – 25y^{2}

= (7x)^{2} – (5y)^{2}

= (7x + 5y) (7x – 5y)

iii) m^{2} – 121

m^{2} -121

= (m)^{2} – (11)^{2}

= (m + 11) (m – 11)

iv) 81 – 64x^{2}

81 – 64x^{2}

= (9)^{2} – (8x)^{2}

= (9 + 8x) (9 – 8x)

v) x^{2}y^{2} – 64

= (xy)^{2} – (8)^{2}

= (xy + 8)(xy – 8)

vi) 6x^{2} – 54

6x^{2} – 54

= 6x^{2} – 6 x 9 ‘

= 6(x^{2} – 9)

= 6[(x)^{2} – (3)^{2}]

= 6(x + 3) (x – 3)

vii) x^{2} – 81

x^{2} – 81

= x^{2} – 9^{2}

= (x + 9 )(x – 9)

viii) 2x – 32 x^{5}

2x – 32 x^{5}

= 2x – 2x x 16x^{4}

= 2 x (1 – 16x^{4})

= 2x [1^{2}) – (4x^{2})^{2}]

= 2x (1 + 4x^{2}) (1 – 4x^{2})

= 2x (1 + 4x^{2}) [(1^{5} – (2x)^{2}]

= 2x (1 + 4x^{2}) (1 + 2x) (1 – 2x)

ix) 81x^{4} – 121x^{2}

81x^{4} – 121x^{2}

– x^{2} (81^{2} – 121)

= x^{2}[(9x)^{2} – (11)^{2}]

= x^{2} (9x + 11) (9x -11)

x) (p^{2} – 2pq + q^{2})-r^{2}

(p^{2} – 2pq + q^{2}) – r^{2}

= (p – q)^{2} – (r)^{2} [∵ p^{2} – 2pq + q^{2} = (p – q)^{2}]

= (p – q + r) (p – q – r)

xi) (x + y)^{2} – (x – y)^{2}

(x + y)^{2} – (x – y)^{2}

It is in the form of a^{2} – b^{2}

a = x + y, b = x- y

∴ a^{2} – b^{2} =(a + b)(a-b)

= (x + y + x – y) [x + y- (x – y)]

= 2x [x + y-x + y]

= 2x x 2y = 4xy

Question 3.

Factorise the expressions

(i) lx^{2} + mx

(ii) 7y^{2} + 35Z^{2}

(iii) 3x^{4} + 6x^{3}y + 9x^{2}Z

(iv) x^{2} – ax – bx + ab

(v) 3ax – 6ay – 8by + 4bx

(vi) mn + m + n + 1

(vii) 6ab – b^{2} + 12ac – 2bc

(viii) p^{2}q – pr^{2} – pq + r^{2}

(ix) x (y + z) -5 (y + z)

(i) lx^{2} + mx

lx^{2} + mx

= l × x × x + m × x = x(lx + m)

(ii) 7y^{2} + 35z^{2}

7y^{2}+ 35z^{2}

= 7 × y^{2} + 7 × 5 × z^{2}

= 7(y^{2} + 5z^{2})

(iii) 3x^{4} + 6x^{3}y + 9x^{2}Z

3x^{4} + 6x^{3}y + 9x^{2}Z

= 3 × x^{2} × x^{2} + 3 × 2 × x × x^{2} × y + 3 × 3 × x^{2} × z

= 3x^{2} (x^{2} + 2xy + 3z)

(iv) x^{2} – ax – bx + ab

x^{2} – ax – bx + ab

= (x^{2} – ax) – (bx – ab)

= x(x – a) – b(x – a)

= (x – a) (x – b)

(v) 3ax – 6ay – 8by + 4bx

3ax – 6ay – 8by + 4bx

= (3ax – 6ay) + (4bx – 8by)

= 3a (x – 2y) + 4b (x – 2y)

= (x – 2y) (3a + 4b)

(vi) mn + m + n + 1

mn + m + n + 1

= (mn + m) + (n + 1)

= m (n + 1) + (n + 1)

= (n + 1) (m + 1)

(vii) 6ab – b^{2} + 12ac – 2bc

6ab – b^{2} + 12ac – 2bc

= (6ab – b^{2}) + (12ac – 2bc)

= (6 × a× b – b × b) + (6 × 2 × a × c – 2 × b × c)

= b [6a – b] + 2c [6a – b]

= (6a – b) (b + 2c)

(viii) p^{2}q – pr^{2} – pq + r^{2}

p^{2}q – pr^{2} – pq + r^{2}

= (p^{2}q – pr^{2}) – (pq – r^{2})

= (p × p × q – p × r × r) – (pq – r^{2})

= P(pq – r^{2}) – (pq – r^{2}) × 1

= (pq – r^{2})(p – 1)

(ix) x (y + z) -5 (y + z)

= x(y + z) – 5(y + z)

= (y + z) (x – 5)

Question 4.

Factorise the following

(i) x^{4} – y^{4}

(ii) a^{4} – (b + c)^{4}

(iii) l^{2} – (m – n)^{2}

(iv) 49x^{2} – 1625

(v) x^{4} – 2x^{2}y^{2} + y^{4}

(vi) 4 (a + b)^{2} – 9 (a – b)^{2}

Solution:

= (x^{2})^{2} – (y^{2})^{2} is in the form of a^{2} – b^{2}

a^{2} – b^{2} = (a + b) (a – b)

x^{4} – y^{4} = (x^{2} + y^{2})(x^{2} – y^{2})

= (x^{2} + y^{2})(x + y)(x – y)

(ii) a^{4} – (b + c)^{4}

a^{4} – (b + c)^{4}

= (a^{2})^{2} – [(b + c)^{2}]^{2}

= [a^{2} + (b + c)^{2}] [a^{2} – (b + c)^{2}] ,

= [a^{2} + (b + c)^{2}] (a + b + c) [a – (b + c)]

= [a^{2} + (b + c)^{2}] (a + b + c) (a – b – c)

(iii) l^{2} – (m – n)^{2}

l^{2} – (m – n)^{2}

= (l)^{2} – (m – n)^{2}

= [l + m – n] [l – (m – n)]

= [l + m -n] [l – m + n]

(iv) 49x^{2} – 1625

= (7x)^{2} – (45)^{2}

= (7x+ (45) (7x – (45)

(v) x^{4} – 2x^{2} y^{2} + y^{4}

= (x^{2} )^{2} – 2x^{2} y^{2} + (y^{2} )^{2}

It is in the form of a^{2} – 2ab + b^{2}

a^{2} – 2ab + b^{2} = (a – b)^{2}

∴ x^{4} – 2x^{2} y^{2} + y^{4} = (x^{2} – y^{2} )^{2}

= [(x)^{2} – (y)^{2} ]^{2}

= [(x + y) (x – y)]^{2}

= (x + y)^{2} (x – y)^{2}

[∵ (ab)^{m} = a ^{m} . b^{n} ]

(vi) 4 (a + b)^{2} – 9 (a – b)^{2}

4 (a + b)^{2} – 9 (a – b)^{2}

= [2(a + b)]^{2} – [3(a – b)]^{2}

= [2(a + b) + 3(a- b)] [2(a + b)-3(a- b)]

= (2a + 2b + 3a – 3b) (2a + 2b – 3a + 3b)

= (5a – b) (5b – a)

Question 5.

Factorise the following expressions

(i) a^{2}+ 10a + 24

(ii) x^{2} +9x + 18

(iii) p^{2} – 10q + 21

(iv) x^{2} – 4x – 32

Solution:

(i) a^{2}+ 10a + 24

a^{2} + 10a + 24 .

= a^{2} + 6a + 4a + 24

= a x a + 6a + 4a + 6 × 4

= a(a + 6) + 4(a + 6)

= (a + 6) (a + 4) (or)

a^{2} + 10a + 24

∴ a^{2} + 10a + 24 = (a + 6) (a + 4)

(ii) x^{2} + 9x + 18

x^{2} + 9x + 18

= (x + 3) (x + 6)

∴ x^{2} + 9x + 18 = (x + 3) (x + 6)

(iii) p^{2} – 10q + 21

p^{2} – 10p + 21

= (P – 7) (p – 3)

∴ p^{2} – 10p + 21 = (p – 7)(p – 3)

(iv) x^{2} – 4x – 32

x^{2} – 4x – 32

= (x – 8) (x + 4)

∴ x^{2} – 4x – 32 = (x – 8) (x + 4)

Question 6.

The lengths of the sides of a triangle are integrals, and its area is also integer. One side is 21 and the perimeter is 48. Find the shortest side.

Solution:

Perimeter of a triangle

= AB + BC + CA = 48

⇒ c + a + b = 48

The solutions of Harmeet, Rosy are wrong.

∴ Srikar had done it correctly.

⇒ 21 + a + b = 48

⇒ a + b = 48 – 21 = 27

∴ The lengths of a, b should be 10, 17

∴ a + b > c [the sum of any two sides of a triangle is greater than the 3rd side]

∴ 10 + 17 > 2

27 > 21 (T).

∴ The length of the shortest side is 10 cm.

Question 7.

Find the values of ‘m’ for which x^{2} + 3xy + x + my – in has two linear factors in x and y, with integer coefficients.

Solution:

Given equation is x^{2} + 3xy + x + my – m ……….(1)

Let the two linear equations in x and y be (x + 3y + a) and (x + 0y + b).

Then (x + 3y + a) (x + 0y + b)

= x^{2} + 0xy + bx + 3xy + 0y^{2} + 3by + ax + 0y + ab

= x^{2} + bx + ax + 3xy + 3by + ab ………….. (2)

Comparing equation (2) with (1),

x^{2} + 3xy + x + my – m

= x^{2} + (a + b)x + 3xy + 3by + ab

Equating the like terms on both sides,

ab = – m ………….. (3)

(a + b)x = x ⇒ a + b = 1 ……………. (4)

3by = my ⇒ 3b = m ⇒ b = m3

Substitute ‘b’ value in equation (4),

a = 1−𝑚3=3−𝑚3

ab = -m

[ ∵ from (3)]

put a & b value then ,

(3−𝑚3)(𝑚3) = -m

3 m−m29= -m

⇒ 3m – m^{2} = – 9m

⇒ m^{2} – 12m = 0

⇒ m(m – 12) = 0

⇒ m = 0 (or) m = 12

lf m = 12

∴ b = 123 = 4&a = 3−m3=3−123

= −93 = -3

∴ Linear factors are (x + 3y – 3), (x + 4) If m = 0

b = 03 = 0 & a = 3−03=33 = 1

∴ Linear factors are (x + 3y + 1), x.

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- AP Board Class 8 Maths Chapter 3 చతుర్భుజాల నిర్మాణాలు InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 4 ఘాతాంకాలు మరియు ఘాతాలు Ex 4.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 4 ఘాతాంకాలు మరియు ఘాతాలు Ex 4.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 4 ఘాతాంకాలు మరియు ఘాతాలు InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 5 అనుపాతముతో రాశులను పోల్చుట Ex 5.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 5 అనుపాతముతో రాశులను పోల్చుట Ex 5.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 5 అనుపాతముతో రాశులను పోల్చుట Ex 5.3 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 5 అనుపాతముతో రాశులను పోల్చుట InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 6 వర్గమూలాలు, ఘనమూలాలు Ex 6.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 6 వర్గమూలాలు, ఘనమూలాలు Ex 6.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 6 వర్గమూలాలు, ఘనమూలాలు Ex 6.3 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 6 వర్గమూలాలు, ఘనమూలాలు Ex 6.4 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 6 వర్గమూలాలు, ఘనమూలాలు Ex 6.5 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 6 వర్గమూలాలు, ఘనమూలాలు InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 7 పౌనఃపున్య విభాజన పట్టికలు, రేఖాచిత్రములు Ex 7.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 7 పౌనఃపున్య విభాజన పట్టికలు, రేఖాచిత్రములు Ex 7.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 7 పౌనఃపున్య విభాజన పట్టికలు, రేఖాచిత్రములు Ex 7.3 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 7 పౌనఃపున్య విభాజన పట్టికలు, రేఖాచిత్రములు InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 8 జ్యామితీయ పటాల అన్వేషణ Ex 8.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 8 జ్యామితీయ పటాల అన్వేషణ Ex 8.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 8 జ్యామితీయ పటాల అన్వేషణ InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 9 సమతల పటముల వైశాల్యములు Ex 9.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 9 సమతల పటముల వైశాల్యములు Ex 9.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 9 సమతల పటముల వైశాల్యములు InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 10 అనులోమ మరియు విలోమ అనుపాతములు Ex 10.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 10 అనులోమ మరియు విలోమ అనుపాతములు Ex 10.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 10 అనులోమ మరియు విలోమ అనుపాతములు Ex 10.3 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 10 అనులోమ మరియు విలోమ అనుపాతములు Ex 10.4 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 10 అనులోమ మరియు విలోమ అనుపాతములు InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 11 బీజీయ సమాసాలు Ex 11.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 11 బీజీయ సమాసాలు Ex 11.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 11 బీజీయ సమాసాలు Ex 11.3 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 11 బీజీయ సమాసాలు Ex 11.4 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 11 బీజీయ సమాసాలు Ex 11.5 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 11 బీజీయ సమాసాలు InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 12 కారణాంక విభజన Ex 12.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 12 కారణాంక విభజన Ex 12.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 12 కారణాంక విభజన Ex 12.3 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 12 కారణాంక విభజన Ex 12.4 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 12 కారణాంక విభజన InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 13 త్రిమితీయ వస్తువులను ద్విమితీయంగా చూపుట Ex 13.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 13 త్రిమితీయ వస్తువులను ద్విమితీయంగా చూపుట Ex 13.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 13 త్రిమితీయ వస్తువులను ద్విమితీయంగా చూపుట InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 14 ఉపరితల వైశాల్యము మరియు ఘనపరిమాణం (ఘనము-దీర్ఘఘనము) Ex 14.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 14 ఉపరితల వైశాల్యము మరియు ఘనపరిమాణం (ఘనము-దీర్ఘఘనము) Ex 14.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 14 ఉపరితల వైశాల్యము మరియు ఘనపరిమాణం (ఘనము-దీర్ఘఘనము) InText Questions Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 15 సంఖ్యలతో ఆడుకుందాం Ex 15.1 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 15 సంఖ్యలతో ఆడుకుందాం Ex 15.2 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 15 సంఖ్యలతో ఆడుకుందాం Ex 15.3 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 15 సంఖ్యలతో ఆడుకుందాం Ex 15.4 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 15 సంఖ్యలతో ఆడుకుందాం Ex 15.5 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 15 సంఖ్యలతో ఆడుకుందాం Ex 15.6 Textbook Solutions PDF
- AP Board Class 8 Maths Chapter 15 సంఖ్యలతో ఆడుకుందాం InText Questions Textbook Solutions PDF

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