Question

If ,(3x-4y)^3=2yx^3-64y^3+axy^2+bx^2y , then find the value of a + b.

Answer 1

${(3x - 4y)}^{3} = 2 7{x}^{3} - 64 {y}^{3} + ax {y}^{2} + b {x}^{2} y \\ \\ expand \: lhs \\ {(3x - 4y)}^{3} \\ \\ = {(3x)}^{3} - {(4y)}^{3} - 3 \times {(3x)}^{2} \times 4y + 3 \times 3x \times {(4y)}^{2} \\ \\ = 27 {x}^{3} - 64 {y}^{3} - 108 {x}^{2} y + 144x {y}^{2}$


$comparing \: with \: \\ 2 7{x}^{3} - 64 {y}^{3} + ax {y}^{2} + b {x}^{2} y \\ \\ a = - 108 \\ \\ b = 144$