Question

1) 2x + y)'3 - 2(y - x)'3

2) (2x - 3)'3 - 2x(2x + 1)'2

3) (3x -1)'2 -27x'2(x + 1)

4) (2x + 1)'3 - 8x(x - 1)'2

Answer 1

1: \(\left(2x+y\right)^3-2\left(y-x\right)^3\)

\(=8x^3+12x^2y+6xy^2+y^3+2\left(x^3-3x^2y+3xy^2-y^3\right)\)

\(=8x^3+12x^2y+6xy^2+y^3+2x^3-6x^2y+6xy^2-2y^3\)

\(=10x^3+6x^2y+12xy^2-y^3\)

2: \(\left(2x-3\right)^3-2x\left(2x+1\right)^2\)

\(=8x^3-36x^2+54x-27-2x\left(4x^2+4x+1\right)\)

\(=8x^3-36x^2+54x-27-8x^3-8x^2-2x\)

\(=-44x^2+52x-27\)

3: \(\left(3x-1\right)^2-27x^2\left(x+1\right)\)

\(=9x^2-6x+1-27x^3-27x^2\)

\(=-27x^3-18x^2-6x+1\)

4: \(\left(2x+1\right)^3-8x\left(x-1\right)^2\)

\(=8x^3+12x^2+6x+1-8x\left(x^2-2x+1\right)\)

\(=8x^3+12x^2+6x+1-8x^3+16x^2-8x\)

\(=28x^2-2x+1\)