Factorise a-2-b-c- - b-c-3-b-c-a-2-b-c-2-b-c-a-2-b-c-2-b-c-a-2-b-c-2-None of these

Question

Toppr Admin · Accepted Answer

Solution- -A- -b-c-a2-x2212-b-c-2-Let b-c-x-x2234-a2-b-c-x2212-b-c-3-a2x-x2212-x3-x21D2-x-a2-x2212-x2-x2235-x-b-c-x2234-a2-b-c-x2212-b-c-3-b-c-a2-x2212-b-c-2-

Factorise $a^{2} (b + c) - (b + c)^{3}$
$(b + c) (a^{2} + (b + c)^{2})$
$(b - c) (a^{2} - (b + c)^{2})$
$(b + c) (a^{2} - (b + c)^{2})$
None of these

Solution:- (A) $(b + c) (a^{2} - {(b + c)}^{2})$
Let $b + c = x$ .
$∴ a^{2} (b + c) - {(b + c)}^{3} = a^{2} x - x^{3}$
$\Rightarrow = x (a^{2} - x^{2})$
$∵ x = b + c$
$∴ a^{2} (b + c) - {(b + c)}^{3} = (b + c) (a^{2} - {(b + c)}^{2})$

Factorise a2(b+c)−(b+c)3(b+c)(a2+(b+c)2)(b−c)(a2−(b+c)2)(b+c)(a2−(b+c)2)None of these

Solution:- (A) (b+c)(a2−(b+c)2)Let b+c=x.∴a2(b+c)−(b+c)3=a2x−x3⇒=x(a2−x2)∵x=b+c∴a2(b+c)−(b+c)3=(b+c)(a2−(b+c)2)

Factorise $a^{2} (b + c) - (b + c)^{3}$
$(b + c) (a^{2} + (b + c)^{2})$
$(b - c) (a^{2} - (b + c)^{2})$
$(b + c) (a^{2} - (b + c)^{2})$
None of these

Solution:- (A) $(b + c) (a^{2} - {(b + c)}^{2})$
Let $b + c = x$ .
$∴ a^{2} (b + c) - {(b + c)}^{3} = a^{2} x - x^{3}$
$\Rightarrow = x (a^{2} - x^{2})$
$∵ x = b + c$
$∴ a^{2} (b + c) - {(b + c)}^{3} = (b + c) (a^{2} - {(b + c)}^{2})$