Solve 4x^2-8x+2left(x+left(2+xright)^2right)

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

Evaluate

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

Solution Steps

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

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

Combine x and 4x to get 5x.

$$4x^{2}-8x+2\left(5x+4+x^{2}\right)$$

Use the distributive property to multiply 2 by 5x+4+x^{2}.

$$4x^{2}-8x+10x+8+2x^{2}$$

Combine -8x and 10x to get 2x.

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

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+2x+8$$

Expand

$$6x^{2}+2x+8$$

Solution Steps

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

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

Combine x and 4x to get 5x.

$$4x^{2}-8x+2\left(5x+4+x^{2}\right)$$

Use the distributive property to multiply 2 by 5x+4+x^{2}.

$$4x^{2}-8x+10x+8+2x^{2}$$

Combine -8x and 10x to get 2x.

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

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+2x+8$$