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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-4\right)^{2}.

$$x^{4}-2x^{2}\left(4x-4\right)+16x^{2}-32x+16$$

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

$$x^{4}-8x^{3}+8x^{2}+16x^{2}-32x+16$$

Combine 8x^{2} and 16x^{2} to get 24x^{2}.

$$x^{4}-8x^{3}+24x^{2}-32x+16$$

Expand

$$x^{4}-8x^{3}+24x^{2}-32x+16$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-4\right)^{2}.

$$x^{4}-2x^{2}\left(4x-4\right)+16x^{2}-32x+16$$

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

$$x^{4}-8x^{3}+8x^{2}+16x^{2}-32x+16$$

Combine 8x^{2} and 16x^{2} to get 24x^{2}.

$$x^{4}-8x^{3}+24x^{2}-32x+16$$