Find the square of the following using identity -
1. $(7 a + b)^{2}$
2. $(71)^{2}$
3. $62 \times 65$
4. $(\frac{3}{5} a - 10 b)^{2}$

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Solution

$(A) (7 a + b)^{2} = 49 a^{2} + b^{2} + 14 a b$
$(B) (71)^{2} = (70 + 1)^{2} = 4900 + 1 + 140$
$(C) 62 \times 65 = (62 \times 65)^{2} = (4030)^{2} = 16, 240, 900$
$(D) {(\frac{3 a}{5} - 10 b)}^{2} = \frac{9 a^{2}}{25} + 100 b^{2} - 2 \times \frac{3 a}{5} \times 10 b^{2}$
$= \frac{3 a^{2}}{25} + 100 b^{2} - 12 a b$

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