Solve (x-4)^2-x(2x-1)^2=

$$( x - 4 ) ^ { 2 } - x ( 2 x - 1 ) ^ { 2 } =$$

Evaluate

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

Solution Steps

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

$$x^{2}-8x+16-x\left(2x-1\right)^{2}$$

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

$$x^{2}-8x+16-x\left(4x^{2}-4x+1\right)$$

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

$$x^{2}-8x+16-\left(4x^{3}-4x^{2}+x\right)$$

To find the opposite of 4x^{3}-4x^{2}+x, find the opposite of each term.

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

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-8x+16-4x^{3}-x$$

Combine -8x and -x to get -9x.

$$5x^{2}-9x+16-4x^{3}$$

Expand

$$16-9x+5x^{2}-4x^{3}$$

Solution Steps

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

$$x^{2}-8x+16-x\left(2x-1\right)^{2}$$

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

$$x^{2}-8x+16-x\left(4x^{2}-4x+1\right)$$

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

$$x^{2}-8x+16-\left(4x^{3}-4x^{2}+x\right)$$

To find the opposite of 4x^{3}-4x^{2}+x, find the opposite of each term.

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

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-8x+16-4x^{3}-x$$

Combine -8x and -x to get -9x.

$$5x^{2}-9x+16-4x^{3}$$