Solve left(x-2right)^2+left(-1-2xright)^2

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

Evaluate

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

Solution Steps

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

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

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

$$x^{2}-4x+4+1+4x+4x^{2}$$

Add 4 and 1 to get 5.

$$x^{2}-4x+5+4x+4x^{2}$$

Combine -4x and 4x to get 0.

$$x^{2}+5+4x^{2}$$

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

$$5x^{2}+5$$

Expand

$$5x^{2}+5$$

Solution Steps

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

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

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

$$x^{2}-4x+4+1+4x+4x^{2}$$

Add 4 and 1 to get 5.

$$x^{2}-4x+5+4x+4x^{2}$$

Combine -4x and 4x to get 0.

$$x^{2}+5+4x^{2}$$

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

$$5x^{2}+5$$