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Factorization Of Algebraic Expressions — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions:
$(a - 2b)^3 - 512b^3$
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Answer

$(a - 2b)^3 - 512b^{3}$
$= (a - 2b)^3 - (8b)^3$
$= (a - 2b - 8b)((a - 2b)^2 + (a - 2b)8b + (8b)^2)$\therefore$ [a^3 - b^3 = (a - b)(a^2 + ab + b^2)]$
$= (a - 10b)(a^2 + 4b^2 - 4ab + 8ab - 16b^2 + 64b^2)$
$= (a - 10b)(a^2 + 52b^2 + 4ab)$
$\therefore$ $(a - 2b)^3 − 512b^3$
$= (a - 10b)(a^2 + 52b^2 + 4ab)$

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