Question
Factorize the following expressions:
$32a^3 + 108b^3$
$32a^3 + 108b^3$
✓
Answer
$32a^3 + 108b^3 $
$= 4(8a^3 + 27b^3)$
$= 4((2a)^3 + (3b)^3)$
$= 4[(2a + 3b)((2a)^2 - 2a \times 3b + (3b)^2$
$\therefore$ $[a^3 + b^3 = (a + b)(a^2 - ab + b^2)]$
$= 4(2a + 3b)(4a^2 - 6ab + 9b^2)$
$\therefore$ $32a^3 + 108b^3 = 4(2a + 3b)(4a^2 - 6ab + 9b^2)$
$= 4(8a^3 + 27b^3)$
$= 4((2a)^3 + (3b)^3)$
$= 4[(2a + 3b)((2a)^2 - 2a \times 3b + (3b)^2$
$\therefore$ $[a^3 + b^3 = (a + b)(a^2 - ab + b^2)]$
$= 4(2a + 3b)(4a^2 - 6ab + 9b^2)$
$\therefore$ $32a^3 + 108b^3 = 4(2a + 3b)(4a^2 - 6ab + 9b^2)$
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