Factorize: 45 a^{3} b + 5 a b^{3} - 30 a^{2} | vedclass

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Question

(C) Given expression: $45 a^{3} b + 5 a b^{3} - 30 a^{2} b^{2}$Step $1$: Take out the common factor $5 a b$ from each term:$= 5 a b(9 a^{2} + b^{2} -

Vedclass · Accepted Answer

$5 a b(3 a - b)^{2}$

Vedclass · Answer

(C) Given expression: $45 a^{3} b + 5 a b^{3} - 30 a^{2} b^{2}$Step $1$: Take out the common factor $5 a b$ from each term:$= 5 a b(9 a^{2} + b^{2} - 6 a b)$Step $2$: Rearrange the terms inside the bracket:$= 5 a b(9 a^{2} - 6 a b + b^{2})$Step $3$: Recognize the expression as a perfect square trinomial of the form $(x - y)^{2} = x^{2} - 2 x y + y^{2}$,where $x = 3 a$ and $y = b$:$= 5 a b((3 a)^{2} - 2(3 a)(b) + (b)^{2})$Step $4$: Apply the identity:$= 5 a b(3 a - b)^{2}$

Factorize: $45 a^{3} b + 5 a b^{3} - 30 a^{2} b^{2}$

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