Question
Factorize the following expressions:
$1 - 27a^3$
$1 - 27a^3$
✓
Answer
$1 - 27a^3$
$= (1)^3 - (3a)^{3}$
$= (1 - 3a)(1^2 + 1 \times 3a + (3a)^2)$
$\therefore$ $[a^3 - b^3 = (a - b)(a^2 + ab + b^2)]$
$= (1 - 3a)(1^2 + 3a + 9a^2)$
$\therefore$ $1 - 27a^3 = (1 - 3a)(1^2 + 3a + 9a^2)$
$= (1)^3 - (3a)^{3}$
$= (1 - 3a)(1^2 + 1 \times 3a + (3a)^2)$
$\therefore$ $[a^3 - b^3 = (a - b)(a^2 + ab + b^2)]$
$= (1 - 3a)(1^2 + 3a + 9a^2)$
$\therefore$ $1 - 27a^3 = (1 - 3a)(1^2 + 3a + 9a^2)$
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