Solve 2x^2left(x+2right)^2+3x^2+6x+1

$$2 { x }^{ 2 } { \left(x+2 \right) }^{ 2 } +3 { x }^{ 2 } +6x+1$$

Evaluate

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

Solution Steps

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

$$2x^{2}\left(x^{2}+4x+4\right)+3x^{2}+6x+1$$

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

$$2x^{4}+8x^{3}+8x^{2}+3x^{2}+6x+1$$

Combine 8x^{2} and 3x^{2} to get 11x^{2}.

$$2x^{4}+8x^{3}+11x^{2}+6x+1$$

Expand

$$2x^{4}+8x^{3}+11x^{2}+6x+1$$

Solution Steps

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

$$2x^{2}\left(x^{2}+4x+4\right)+3x^{2}+6x+1$$

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

$$2x^{4}+8x^{3}+8x^{2}+3x^{2}+6x+1$$

Combine 8x^{2} and 3x^{2} to get 11x^{2}.

$$2x^{4}+8x^{3}+11x^{2}+6x+1$$