Question
Factorise:
$a^2-b^2-4 a c+4 c^2$
$a^2-b^2-4 a c+4 c^2$
✓
Answer
$a^2-4 a c+4 c^2-b^2$
$=a^2-4 a c+4 c^2-b^2$
$=a^2-2 \times a \times 2 c+(2 c)^2-b^2$
$=(a-2 c)^2-b^2\left[\therefore a^2-b^2=(a-b)(a+b)\right]$
$=(a-2 c+b)(a-2 c-b)$
$=a^2-4 a c+4 c^2-b^2$
$=a^2-2 \times a \times 2 c+(2 c)^2-b^2$
$=(a-2 c)^2-b^2\left[\therefore a^2-b^2=(a-b)(a+b)\right]$
$=(a-2 c+b)(a-2 c-b)$
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