Factorise the following- -a-b-3-a-b-32b-3a-2 - b-2-b-3a - b-2-2b-3a - b-b-3a-2 - b-

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Toppr Admin · Accepted Answer

-a-b-3-x2212-a-x2212-b-3Using-a3-x2212-b3-a-x2212-b-a2-ab-b2-a-b-x2212-a-x2212-b-a-b-2-a-b-a-x2212-b-a-x2212-b-2-a-b-x2212-a-b-a2-2ab-b2-a2-x2212-ab-ab-x2212-b2-a2-x2212-2ab-b2-2b-3a2-b2-

Factorise the following: $(a + b)^{3} - (a - b)^{3}$
$2 b (3 a^{2} + b^{2})$
$b (3 a + b^{2})$
$2 b (3 a - b)$
$b (3 a^{2} + b)$

$(a + b)^{3} - (a - b)^{3}$
Using, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$= [(a + b) - (a - b)] [(a + b)^{2} + (a + b) (a - b) + (a - b)^{2}]$
$= (a + b - a + b) [a^{2} + 2 a b + b^{2} + a^{2} - a b + a b - b^{2} + a^{2} - 2 a b + b^{2}]$
$= 2 b (3 a^{2} + b^{2})$

Factorise the following: (a+b)3−(a−b)32b(3a2+b2)b(3a+b2)2b(3a−b)b(3a2+b)

(a+b)3−(a−b)3Using,a3−b3=(a−b)(a2+ab+b2)=[(a+b)−(a−b)][(a+b)2+(a+b)(a−b)+(a−b)2]=(a+b−a+b)[a2+2ab+b2+a2−ab+ab−b2+a2−2ab+b2]=2b(3a2+b2)

Factorise the following: $(a + b)^{3} - (a - b)^{3}$
$2 b (3 a^{2} + b^{2})$
$b (3 a + b^{2})$
$2 b (3 a - b)$
$b (3 a^{2} + b)$

$(a + b)^{3} - (a - b)^{3}$
Using, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$= [(a + b) - (a - b)] [(a + b)^{2} + (a + b) (a - b) + (a - b)^{2}]$
$= (a + b - a + b) [a^{2} + 2 a b + b^{2} + a^{2} - a b + a b - b^{2} + a^{2} - 2 a b + b^{2}]$
$= 2 b (3 a^{2} + b^{2})$