Question
Factorise the following by grouping the terms:$4abx^2 + 49aby^2 + 14xy(a^2 + b^2)$
✓
Answer
$4abx^2 + 49aby^2 + 14xy(a^2 + b^2)$
$= 4abx^2 + 49aby^2 + 14a^2xy + 14b^2xy$
$= (4abx^2 + 14a^2xy) + (14b^2xy + 49aby^2)$
$= 2ax(2bx + 7ay) + 7by(2bx + 7ay)$
$= (2bx + 7ay)(2ax + 7by).$
$= 4abx^2 + 49aby^2 + 14a^2xy + 14b^2xy$
$= (4abx^2 + 14a^2xy) + (14b^2xy + 49aby^2)$
$= 2ax(2bx + 7ay) + 7by(2bx + 7ay)$
$= (2bx + 7ay)(2ax + 7by).$
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