Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$\frac{2\text{p}^2}{25}-32\text{q}^2$
$\frac{2\text{p}^2}{25}-32\text{q}^2$
✓
Answer
$\frac{2\text{p}^2}{25}-32\text{q}^2$$= 2\Big(\frac{\text{p}^2}{25}-16\text{q}^2\Big)$
$=2\Big[\Big(\frac{\text{p}^2}{5}\Big)-\big(4\text{q}^2\big)\Big]$
$=2\Big(\frac{\text{p}}{5}+4\text{q}\Big)\Big(\frac{\text{p}}{5}-4\text{q}\Big)$
$=2\Big[\Big(\frac{\text{p}^2}{5}\Big)-\big(4\text{q}^2\big)\Big]$
$=2\Big(\frac{\text{p}}{5}+4\text{q}\Big)\Big(\frac{\text{p}}{5}-4\text{q}\Big)$
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