Question
Factorize the following expressions:
$8a^3 - b^3 - 4ax + 2bx$
$8a^3 - b^3 - 4ax + 2bx$
✓
Answer
$= (2a)^3 - b^3 - 2x(2a - b)$
$= (2a - b)((2a)^2 + 2a \times b + b^2) - 2x(2a - b)$
$\big[\therefore$ $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$\big]$
$= (2a - b)(4a^2 + 2ab + b^2- 2x)$
$\therefore$ $8a^3 - b^3 - 4ax + 2bx$
$ = (2a - b)(4a^2 + 2ab + b^2 - 2x)$
$= (2a - b)((2a)^2 + 2a \times b + b^2) - 2x(2a - b)$
$\big[\therefore$ $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$\big]$
$= (2a - b)(4a^2 + 2ab + b^2- 2x)$
$\therefore$ $8a^3 - b^3 - 4ax + 2bx$
$ = (2a - b)(4a^2 + 2ab + b^2 - 2x)$
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