Factorize- 75 a - b 2-48 a - b 2A- 3 a -9 b 9 a - b B- 3 a -3 b 3 a - b C- 3 a -9 b 9 a - b D- 3 a -9 b 9 a - b

The correct option is A 3(a + 9b)(9a + b)) 75(a+b)^2 48(a b)^2= nbsp;3{25(a+b)^2 16(a b)^2} = nbsp;3{[5(a+b)]^2 [4(a b)]^2} Using the identity:a^2 b ...

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Byju's Answer

Standard IX

Mathematics

Factorization of Expressions Reducible to Difference of Two Squares

Factorize: 75...

Question

Factorize: $75 (a + b)^{2} - 48 (a - b)^{2}$ .

$3 (a + 9 b) (9 a + b))$

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$3 (a - 9 b) (9 a - b))$

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$3 (a + 3 b) (3 a + b))$

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$3 (a - 9 b) (9 a + b))$

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Solution

The correct option is A
$3 (a + 9 b) (9 a + b))$

$75 (a + b)^{2} - 48 (a - b)^{2} = 3 {25 (a + b)^{2} - 16 (a - b)^{2}}$
$= 3 {[5 (a + b)]^{2} - [4 (a - b)]^{2}}$

Using the identity: $a^{2} - b^{2} = (a - b) (a + b)$
$= 3 {[5 (a + b) - 4 (a - b)] [5 (a + b) + 4 (a - b)]}$

$= 3 {(5 a + 5 b - 4 a + 4 b) (5 a + 5 b + 4 a - 4 b)}$

$\Rightarrow 3 (a + 9 b) (9 a + b)$

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Similar questions

Q. Factorize:

1 - 2 a - 2 b - 3 (a + b)^{2}

Factorize: 125a³ – 27b³ – 225a²b + 135ab².

Q. The expression (a − b)³ + (b − c)³ + (c −a)³ can be factorized as

(a) (a − b) (b − c) (c −a)

(b) 3(a − b) (b − c) (c −a)

(c) −3(a − b) (b −c) (c − a)

(d) (a + b + c) (a² + b² + c² − ab − bc − ca)

\frac{(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3} + (c^{2} - a^{2})^{3}}{(a - b)^{3} + (b - c)^{3} + (c - a)^{3}} =

(a) 3(a + b) ( b+ c) (c + a)

(b) 3(a − b) (b − c) (c − a)

(c) (a − b) (b − c) (c − a)

(d) none of these

Q. Factorize :

1 - 2 a - 2 b - 3 (a + b)^{2}

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Factorize: 75(a+b)2−48(a−b)2.

The correct option is A 3(a+9b)(9a+b)) 75(a+b)2−48(a−b)2=3{25(a+b)2−16(a−b)2} =3{[5(a+b)]2−[4(a−b)]2} Using the identity:a2−b2=(a−b)(a+b) =3{[5(a+b)−4(a−b)][5(a+b)+4(a−b)]} =3{(5a+5b−4a+4b)(5a+5b+4a−4b)} ⇒3(a+9b)(9a+b)

Factorize: $75 (a + b)^{2} - 48 (a - b)^{2}$ .