Question
Factorise the following by taking out the common factors:$5a(x^2 - y^2) + 35b(x^2 - y^2)$
✓
Answer
$5 a\left(x^2-y^2\right)+35 b\left(x^2-y^2\right)$
Here, the common factor is $5\left(x^2-y^2\right)$.
Dividing throughout by $5\left(x^2-y^2\right)$.
we get
$\frac{5 a\left(x^2-y^2\right)}{5\left(x^2-y^2\right)}+\frac{35 b\left(x^2-y^2\right)}{5\left(x^2-y^2\right)} $
$=a+7 b $
$\therefore 5 a\left(x^2-y^2\right)+35 b\left(x^2-y^2\right) $
$=5\left(x^2-y^2\right)(a+7 b) .$
Here, the common factor is $5\left(x^2-y^2\right)$.
Dividing throughout by $5\left(x^2-y^2\right)$.
we get
$\frac{5 a\left(x^2-y^2\right)}{5\left(x^2-y^2\right)}+\frac{35 b\left(x^2-y^2\right)}{5\left(x^2-y^2\right)} $
$=a+7 b $
$\therefore 5 a\left(x^2-y^2\right)+35 b\left(x^2-y^2\right) $
$=5\left(x^2-y^2\right)(a+7 b) .$
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