Question

a,(2x-3)^3-(x-1)^3-2(x-2)(x+2)

b,(x-3)^2-2.(x+2)^3-4(x+3)(x-3)

c,(2x-5)^3-4(x-2)(x+2)-2(x+1)^3

 

Answer 1

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

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

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

\(=7x^3+37x^2+24x+36\)

\(b,\left(x-3\right)^2-2\left(x+2\right)^3-4\left(x+3\right)\left(x-3\right)\)

\(=x^2-6x+9-2\left(x^3+6x^2+12x+8\right)-4\left(x^2-9\right)\)

\(=x^2-6x+9-2x^3-12x^2-24x-16-4x^2+36\)

\(=-15x^2-30x-2x^3+45\)

\(c,\left(2x-5\right)^3-4\left(x-2\right)\left(x+2\right)-2\left(x+1\right)^3\)

\(=8x^3-10x^2+50x-25-4\left(x^2-4\right)-2\left(x^3+3x^2+3x+1\right)\)

\(=8x^3-10x^2+50x-25-4x^2+16-2x^3-6x^2-6x-2\)

\(=6x^3-20x^2+44x-11\)