Question
Factorise the following:$7(x - 2)^2 - 13(x - 2) - 2$
✓
Answer
$7(x - 2)^2 - 13(x - 2) - 2$
$= 7(x - 2)^2 - 14(x - 2) + (x - 2) - 2$
$= 7(x - 2)(x - 2 - 2) + 1(x - 2 - 2)$
$= 7(x - 2)(x - 4) + 1(x - 4)$
$= (x - 4)[7(x - 2) + 1]$
$= (x - 4)(7x - 14 + 1)$
$= (x - 4)(7x - 13).$
$= 7(x - 2)^2 - 14(x - 2) + (x - 2) - 2$
$= 7(x - 2)(x - 2 - 2) + 1(x - 2 - 2)$
$= 7(x - 2)(x - 4) + 1(x - 4)$
$= (x - 4)[7(x - 2) + 1]$
$= (x - 4)(7x - 14 + 1)$
$= (x - 4)(7x - 13).$
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