Factorise the following expressions-i p2-q2- ii 4 x2-25 y2 iii y2-4 iv p2-125 -v 9 x2-116 y 2 vi x2-1 x 2 vii a2 b-a b viii 4 x2 y-6 x2ix 12 y 2-8 z 2 x 2 x 2-8 y 2

i #160;p2 q2=p2 q2=p+qp q #160; #160; #160; #160; #8757; #160;a+ba b=a2 b2 (ii) #160;4x2 25y2=2x2 5y2=2x+5y2x 5y #160; #160; #160; #160 ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation by Regrouping Terms

Factorise the...

Question

Factorise the following expressions.
(i) p ²-q ² (ii) 4x² - 25y²(iii) y² - 4 (iv) p²- $\frac{1}{25}$
(v) 9x²- $\frac{1}{16 y 2}$
(vi) $12 y^{2} - 8 z^{2}$

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Solution

$(i) p^{2} - q^{2} = (p - q) (q + p) [∵ a^{2} - b^{2} = (a - b) (a + b)]$
$(i i) 4 x^{2} - 25 y^{2} = (2 x)^{2} - (5 y)^{2} = (2 x - 5 y) (2 x + 5 y) [∵ a^{2} - b^{2} = (a - b) (a + b)]$

$(i i i) y^{2} - 4 = y^{2} - 2^{2} = (y - 2) (y + 2) [∵ a^{2} - b^{2} = (a - b) (a + b)]$

$(i v) p^{2} - \frac{1}{25} = 5^{2} p^{2} - 1 = (5 p)^{2} - (1)^{2} (5 p - 1) (5 p + 1) [∵ a^{2} - b^{2} = (a - b) (a + b)]$

$(v) 9 x^{2} - \frac{1}{16 y^{2}} = (12 x y)^{2} - (1)^{2} = (112 x y - 1) (112 x y + 1) [∵ a^{2} - b^{2} = (a - b) (a + b)]$

$(v i) 12 y^{2} - 8 z^{2} = (2 \sqrt 3 y)^{2} - (2 \sqrt 2 z)^{2} = (2 \sqrt 3 y - 2 \sqrt 2 z) (2 \sqrt 3 y + 2 \sqrt 2 z) [∵ a^{2} - b^{2} = (a - b) (a + b)]$

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Similar questions

Q. Factorise the following expressions.
(i)

a^{2} + 8 a + 16

(ii)

p^{2} - 10 p + 25

(iii)

25 m^{2} + 30 m + 9

(iv)

49 y^{2} + 84 y z + 36 z^{2}

(v)

4 x^{2} - 8 x + 4

(vi)

121 b^{2} - 88 b c + 16 c^{2}

(vii)

(l + m)^{2} - 4 l m

(viii)

a^{4} + 2 a^{2} b^{2} + b^{4}

Q. Factorise the following expressions.
(i)

p^{2} + 6 p + 8

(ii)

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Q. Factorise each of the following expressions:
(i)

16 x^{2} + 24 x y + 9 y^{2}

(ii)

y^{2} + 6 x y + 9 x^{2}

(iii)

2 x^{2} - 4 x + 2

(iv)

20 x^{2} + 100 x + 125

(v)

a^{2} + 6 a b + 9 b^{2} - c^{2}

(vi)

x^{2} - y^{2} + 6 x + 9

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m^{2} - 4 n^{2} + 10 m + 25

(viii)

27 a^{2} + 72 a b + 48 b^{2}

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49 y^{2} - 70 y z + 25 z^{2}

(x)

121 x^{2} - 154 x y + 49 y^{2}

(xi)

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Factories the following expressions.
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(v)

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(vi)

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(vii)

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(viii)

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(ix)

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(x)

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Q. Factorise the following numbers into primes.
(i) 32
(ii) 57
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(iv) 150
(v) 216
(vi) 208
(vii) 765
(viii) 342
(ix) 377
(x) 559

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Factorise the following expressions.(i) p 2-q 2 (ii) 4x2 - 25y2 (iii) y2 - 4 (iv) p2 - 125(v) 9x2 -116y2(vi) 12y2−8z2

Factorise the following expressions.
(i) p ²-q ² (ii) 4x² - 25y²(iii) y² - 4 (iv) p²- $\frac{1}{25}$
(v) 9x²- $\frac{1}{16 y 2}$
(vi) $12 y^{2} - 8 z^{2}$