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

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

Evaluate

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

Solution Steps

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

$$\left(x^{2}\right)^{2}-8x^{2}x+16x^{2}-x^{2}+4x-2$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Combine 16x^{2} and -x^{2} to get 15x^{2}.

$$x^{4}-8x^{3}+15x^{2}+4x-2$$

Expand

$$x^{4}-8x^{3}+15x^{2}+4x-2$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-8x^{2}x+16x^{2}-x^{2}+4x-2$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Combine 16x^{2} and -x^{2} to get 15x^{2}.

$$x^{4}-8x^{3}+15x^{2}+4x-2$$