Question
Factorise the following by grouping the terms:$2a + b + 3c - d + (2a + b)^3 + (2a + b)^2(3c - d)$
✓
Answer
$2a + b + 3c - d + (2a + b)^3 + (2a + b)^2(3c - d)$
$= (2a + b + 3c - d) + [(2a + b)^3 + (2a + b)^2(3c - d)]$
$= 1(2a + b + 3c - d) + (2a + b)^2(2a + b + 3c - d)$
$= (2a + b + 3c - d)[1 + (2a + b)^2].$
$= (2a + b + 3c - d) + [(2a + b)^3 + (2a + b)^2(3c - d)]$
$= 1(2a + b + 3c - d) + (2a + b)^2(2a + b + 3c - d)$
$= (2a + b + 3c - d)[1 + (2a + b)^2].$
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