Simplify: (7 9 a+9 7 b )^2-ab - Vidyadip

Question

Simplify:$\big(\frac{7}{9}\text{a}+\frac{9}{7}\text{b}\Big)^2-\text{ab}$

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Answer

$\big(\frac{7}{9}\text{a}+\frac{9}{7}\text{b}\Big)^2-\text{ab}$$=\Big(\frac{7}{9}\text{a}\Big)^2+\Big(\frac{9}{7}\text{b}\Big)^2+2\times\frac{7}{9}\text{a}\times\frac{9}{7}\text{b}-\text{ab}$
$=\frac{49}{81}\text{a}^2+\frac{81}{49}\text{b}^2+2\text{ab}-\text{ab}$
$=\frac{49}{81}\text{a}^2+\text{ab}+\frac{81}{49}\text{b}^2$

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