Question

Show that
(6/5m-5/6n)²+4mn=(6/5m+5/6n)​

Answer 1

Step-by-step explanation:

$( \frac{6}{5}m - \frac{5}{6}n) {}^{2} + 4mn \\ = (\frac{6}{5}m) {}^{2} - 2mn + ( \frac{5}{6}n) {}^{2} + 4mn \\ = ( \frac{6}{5}m) {}^{2} +2mn + ( \frac{5}{6}n) {}^{2} \\ = ( \frac{6}{5}m + \frac{5}{6}n) {}^{2}$

$the \: formulas \: used \: here \: are \\ (x + y) {}^{2} = x {}^{2} + y {}^{2} + 2xy \\ (x - y) {}^{2} = x {}^{2} + y {}^{2} - 2xy$

$hence \: proved.$