Solve 4left(x+2yright)^2+4(x+2y)+1

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

Evaluate

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

Solution Steps

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

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

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

$$4x^{2}+16xy+16y^{2}+4\left(x+2y\right)+1$$

Use the distributive property to multiply 4 by x+2y.

$$4x^{2}+16xy+16y^{2}+4x+8y+1$$

Expand

$$4x^{2}+16xy+4x+16y^{2}+8y+1$$

Solution Steps

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

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

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

$$4x^{2}+16xy+16y^{2}+4\left(x+2y\right)+1$$

Use the distributive property to multiply 4 by x+2y.

$$4x^{2}+16xy+16y^{2}+4x+8y+1$$