Question

Question 92 (xvii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$\frac{1}{36}{a}^2{b}^2-\frac{16}{49}{b}^2{c}^2$

Answer 1

$\frac{1}{36}{a}^2{b}^2-\frac{16}{49}{b}^2{c}^2={\left(\frac{ab}{6}\right)}^2-{\left(\frac{4bc}{7}\right)}^2=(\frac{ab}{6}+\frac{4bc}{7})(\frac{ab}{6}-\frac{4bc}{7})=b^2(\frac{a}{6}+\frac{4c}{7})(\frac{a}{6}-\frac{4c}{7})$