Question

please answer these questions with solutions​

Answer 1

Solution-

1. (3x+2y)^2=9x^2+4y^2+6xy

Answer 2

$i. \: (3x + 2y) {}^{2} = (3 x) {}^{2} + (2y) {}^{2} + \\ \: \: \: \: 2.3x.2y = 9x {}^{2} + 4y {}^{2} + 12xy \\ ii. \: (\frac{2}{3} a + \frac{3}{4} b) {}^{2} = \: (\frac{2}{3}a ) {}^{2} + (\frac{3}{4} b) {}^{2} + \\ \: \: \: \: \: 2. \frac{2}{3} a. \frac{3}{4} b = \frac{4}{9} {a}^{2} + \frac{9}{16} {b}^{2} + ab \\ iii.( 4x - 7y) {}^{2} = (4x ) {}^{2} + (7y) {}^{2} - \\ \: \: \: \: \: 2.4x.7y = 16x {}^{2} + 49y {}^{2} - 56xy \\ iv.( \frac{3}{4}p - \frac{5}{6} q) {}^{2} = ( \frac{3}{4} p) {}^{2} + ( \frac{5}{6} q) {}^{2} - \\ \: \: \: \: \: \: \:2. \frac{3}{4} p. \frac{5}{6} q = \frac{9}{16} {p}^{2} + \frac{25}{36} {q}^{2} - \\ \: \: \: \: \: \frac{5}{4} pq \\ v.(4x + 5y)(4x - 5y) = (4x) {}^{2} - \\ \: \: \: \: \:(5y) {}^{2} = 16x {}^{2} - 25y {}^{2} \\ vi.(3x {}^{2} + 2y {}^{2} )(3x {}^{2} - 2y {}^{2} ) = \\ \: \: \: \: \: \: \: (3x {}^{2} ) {}^{2} - (2y {}^{2} ) {}^{2} = 3x {}^{4} - 2y {}^{4}$

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