Question

1) x³+3x²y-7x+3xy²-7y+y³

2) 625x⁴-81y⁴

3) 64x⁶-y⁶

4) x²-a²+4xy+6ab+4y²-9b²

5) 25x²-49y²+10ax-14ay+15bx-21by

 

Answer 1

\(1,=\left(x^3+3x^2y+3xy^2+y^3\right)-7\left(x+y\right)\\ =\left(x+y\right)^3-7\left(x+y\right)\\ =\left(x+y\right)\left[\left(x+y\right)^2-7\right]\\ 2,=\left(25x^2-9y^2\right)\left(25x^2+9y^2\right)\\ 3,=\left(4x^2-y^2\right)\left(16x^2+4x^2y^2+y^2\right)\\ 4,=\left(x^2+4xy+4y^2\right)-\left(a^2-6ab+9b^2\right)\\ =\left(x+y\right)^2-\left(a-3b\right)^2\\ =\left(x+y-a+3b\right)\left(x+y+a-3b\right)\\ e,=\left(5x-7y\right)\left(5x+7y\right)+2a\left(5x-7y\right)+3b\left(5x-7y\right)\\ =\left(5x-7y\right)\left(5x+7y+2x+3b\right)\)