Question

1) A=(2x-1)^3-(x+1)^3

2) B=(2x+3)^3+(1-2x)^3

3) C=(3x+3)^2-2(x+1)^3-(5x-1)^2

4) D=(-2x+3)^3-(x+1)^3+(3x-1)^2

5) E=(x+1)^3+3(x+1)^2(x-1)+3(x+1)(x-1)^2+(x-1)^3

Answer 1

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

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

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

\(=7x^3-15x^2+3x-2\)

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

\(=8x^3+36x^2+54x+27+1-6x+12x^2-8x^3\)

\(=48x^2+48x+28\)

3: \(C=\left(3x+2\right)^2-2\left(x+1\right)^3-\left(5x-1\right)^2\)

\(=9x^2+12x+4-2\left(x^3+3x^2+3x+1\right)-\left(25x^2-10x+1\right)\)

\(=9x^2+12x+4-2x^3-6x^2-6x-2-25x^2+10x-1\)

\(=-2x^3-22x^2+16x+1\)

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

\(=-8x^3+36x^2-54x+27-x^3-3x^2-3x-1+9x^2-6x+1\)

\(=-9x^3+42x^2-63x+27\)

5: \(E=\left(x+1\right)^3+3\left(x+1\right)^2\cdot\left(x-1\right)+3\left(x+1\right)\left(x-1\right)^2+\left(x-1\right)^3\)

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