\(a,=\left(x+8-x+2\right)^2=10^2=100\\ b,=x^2\left(x^2-16\right)-\left(x^4-1\right)=x^4-16x^2-x^4+1=1-16x^2\\ c,=x^3+1-x^3+1=2\)

\(a,x^2+4x-21-x^2-4x+5=-16\\ b,=\left(x+8-x+2\right)^2=10^2=100\\ c,=x^2\left(x^2-16\right)-\left(x^4-1\right)\\ =x^4-16x^2-x^4+1=1-16x^2\\ d,=x^3+1-x^3+1=2\)

\(a,=x^2+4x-21-x^2-4x+5=-16\\ b,=\left(x+8-x+2\right)^2=10^2=100\\ c,=x^2\left(x^2-16\right)-\left(x^4-1\right)\\ =x^4-16x^2-x^4+1=1-16x^2\\ d,=x^3+1-x^3+1=2\)

A) -2x(3x+2)(3x-2)+5(x+2)² - (x-1)(2x+1)(2x+1)

= -2x(9x²-4)+5(x²+4x+4) - (x-1)(4x²-1)

= -18x³+8x+5x²+20x+20-(4x³-x-4x²+1)

= -18x³+5x²+28x+20-4x³+x+4x²+1

= -22x³+9x²+29x+21

B) (7x-8)(7x+8)-10(2x+3)²+5x(3x-2)²-4x(x-5)²

= 49x² - 64 -10(4x²+ 12x + 3) + 5x(9x² - 12x +4) - 4x(x² - 10x +25)

= 49x² - 64 -40x² - 120x - 30 + 45x³ - 60x² - 20x - 4x³ + 40x² -100x

= 41x³ -11x² -240x -94

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

\(\left(x^4-9\right)-5x^2\left(x^2+2x+1\right)-\left(x^4-2x^3-3x^3+6x^2\right)+4x\left(x^2+4x+4\right)\)

\(x^4-9-5x^4-10x^3-5x^2-x^4+5x^3-6x^2+4x^3+16x^2+16x\)

\(-5x^4-x^3+5x^2+20x-9\)

D) \(-6x^2\left(x+5\right)^2-\left(x-3\right)^2+\left(x^2-2\right)\left(2x^2+1\right)-4x^2\left(3x-4\right)^2\)

\(-6x^2\left(x^2+10x+25\right)-\left(x^2-6x+9\right)+2x^4-3x^2-2-4x^2\left(9x^2-24x+16\right)\)

\(-6x^4-60x^3+150x^2-x^2+6x-9+2x^4-3x^2-2-36x^4+96x^3-64x^2\)

\(-40x^4+36x^3+82x^2+6x-11\)

\(=x^2+6x+5+x^3-8-x^3-x^2+2x=8x-3\)

\(=x^2+6x+5+x^3-8-x^3-x^2+2x=8x-3\)

1/2  x 2 (6x – 3) – x(  x 2 + 1/2) + 1/2.(x + 4)

= (3 x 3  – 3/2. x 2 ) – ( x 3  + 1/2.x) + (1/2.x + 2)

= 3 x 3  - 3/2  x 2  –  x 3  - 1/2 x + 1/2 x + 2

= ( 3 x 3  –  x 3  ) - 3/2.  x 2  – (1/2 x - 1/2 x) + 2

= 2 x 3  - 3/2  x 2  + 2

\(A=x^2+4x-21-x^2-4x+5=-16\\ B=-2\left(4x^2+20x+25\right)-\left(1-16x^2\right)\\ B=-8x^2-40x-50-1+16x^2=8x^2-40x-51\\ C=x^2\left(x^2-16\right)-\left(x^4-1\right)=x^4-16x^2-x^4+1=1-16x^2\\ D=x^3+1-\left(x^3-1\right)=2\\ E=x^3-3x^2+3x-1-x^3+1-9x^2+1=-12x^2+3x+1\)

a) Ta có: \(\left(x+2y\right)\left(x^2-2xy+4y^2\right)-\left(x-y\right)\left(x^2+xy+y^2\right)\)

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

\(=x^3+8y^3-x^3+y^3\)

\(=9y^3\)

b) Ta có: \(\left(x+1\right)\left(x-1\right)^2-\left(x+2\right)\left(x^2-2x+4\right)\)

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

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

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

\(=-x^2-x-7\)