Factorization Of Algebraic Expressions — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions:
$a^3+8 b^3+64 c^3-24 a b c$
✓
Answer
$a^3+8 b^3+64 c^3-24 a b c$
$=(a)^3+(2 b)^3+(4 c)^3-3 \times 2 b \times 4 c$
$=(a+2 b+4 c)\left(a^2+(2 b)^2+(4 c)^2-a \times 2 b-2 b \times 4 c-4 c \times a\right)$
${\left[\because a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)\right]}$
$=(a+2 b+4 c)\left(a^2+4 b^2+16 c^2-2 a b-8 b c-4 a c\right)$
$\therefore a^3+8 b^3+64 c^3-24 a b c=(a+2 b+4 c)\left(a^2+4 b^2+16 c^2-2 a b-8 b c-4 a c\right)$
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