Solve x(2x+5)(5-2x)-4x(x-1)^2

$$x ( 2 x + 5 ) ( 5 - 2 x ) - 4 x ( x - 1 ) ^ { 2 }$$

Evaluate

$$x\left(21+8x-8x^{2}\right)$$

Solution Steps

Use the distributive property to multiply x by 2x+5.

$$\left(2x^{2}+5x\right)\left(5-2x\right)-4x\left(x-1\right)^{2}$$

Use the distributive property to multiply 2x^{2}+5x by 5-2x and combine like terms.

$$-4x^{3}+25x-4x\left(x-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-4x^{3}+25x-4x\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply -4x by x^{2}-2x+1.

$$-4x^{3}+25x-4x^{3}+8x^{2}-4x$$

Combine -4x^{3} and -4x^{3} to get -8x^{3}.

$$-8x^{3}+25x+8x^{2}-4x$$

Combine 25x and -4x to get 21x.

$$-8x^{3}+21x+8x^{2}$$

Expand

$$21x+8x^{2}-8x^{3}$$

Solution Steps

Use the distributive property to multiply x by 2x+5.

$$\left(2x^{2}+5x\right)\left(5-2x\right)-4x\left(x-1\right)^{2}$$

Use the distributive property to multiply 2x^{2}+5x by 5-2x and combine like terms.

$$-4x^{3}+25x-4x\left(x-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-4x^{3}+25x-4x\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply -4x by x^{2}-2x+1.

$$-4x^{3}+25x-4x^{3}+8x^{2}-4x$$

Combine -4x^{3} and -4x^{3} to get -8x^{3}.

$$-8x^{3}+25x+8x^{2}-4x$$

Combine 25x and -4x to get 21x.

$$-8x^{3}+21x+8x^{2}$$