Solve x^2+4x(x+3y)+4(x+3y)^2=

$$x ^ { 2 } + 4 x ( x + 3 y ) + 4 ( x + 3 y ) ^ { 2 } =$$

Evaluate

$$9\left(x+2y\right)^{2}$$

Solution Steps

Use the distributive property to multiply 4x by x+3y.

$$x^{2}+4x^{2}+12xy+4\left(x+3y\right)^{2}$$

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

$$5x^{2}+12xy+4\left(x+3y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3y\right)^{2}.

$$5x^{2}+12xy+4\left(x^{2}+6xy+9y^{2}\right)$$

Use the distributive property to multiply 4 by x^{2}+6xy+9y^{2}.

$$5x^{2}+12xy+4x^{2}+24xy+36y^{2}$$

Combine 5x^{2} and 4x^{2} to get 9x^{2}.

$$9x^{2}+12xy+24xy+36y^{2}$$

Combine 12xy and 24xy to get 36xy.

$$9x^{2}+36xy+36y^{2}$$

Expand

$$9x^{2}+36xy+36y^{2}$$

Solution Steps

Use the distributive property to multiply 4x by x+3y.

$$x^{2}+4x^{2}+12xy+4\left(x+3y\right)^{2}$$

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

$$5x^{2}+12xy+4\left(x+3y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3y\right)^{2}.

$$5x^{2}+12xy+4\left(x^{2}+6xy+9y^{2}\right)$$

Use the distributive property to multiply 4 by x^{2}+6xy+9y^{2}.

$$5x^{2}+12xy+4x^{2}+24xy+36y^{2}$$

Combine 5x^{2} and 4x^{2} to get 9x^{2}.

$$9x^{2}+12xy+24xy+36y^{2}$$

Combine 12xy and 24xy to get 36xy.

$$9x^{2}+36xy+36y^{2}$$