Factorise the following using the identity a^2- b^2= (a + b)(a - b). 1 36 a^2b^2-16 49 b^2c^2

1 36 a^2b^2-16 49 b^2c^2= ( ab 6 )^2- ( 4bc 7 )^2 = ( ab 6 + 4bc 7 ) =b^2 ( a 6 + 4c 7 ) ( a 6 - 4c 7 )

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

Question

Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$\frac{1}{36}\text{a}^2\text{b}^2-\frac{16}{49}\text{b}^2\text{c}^2$

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Answer

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

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