Question 85 (iii)

Expand the following, using suitable identities.

${(\frac{4}{5} a + \frac{5}{4} b)}^{2}$

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Solution

We have,
${(\frac{4}{5} a + \frac{5}{4} b)}^{2} = {(\frac{4}{5} a)}^{2} + {(\frac{5}{4} b)}^{2} + 2 \times \frac{4}{5} a \times \frac{5}{4} b$
$= \frac{16}{25} a^{2} + \frac{25}{16} b^{2} + 2 a b$ [using the identity, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ ]

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