Solve x^2+10x(x+3y)+25(x+3y)^2=

$$x ^ { 2 } + 10 x ( x + 3 y ) + 25 ( x + 3 y ) ^ { 2 } =$$

Evaluate

$$9\left(2x+5y\right)^{2}$$

Solution Steps

Use the distributive property to multiply 10x by x+3y.

$$x^{2}+10x^{2}+30xy+25\left(x+3y\right)^{2}$$

Combine x^{2} and 10x^{2} to get 11x^{2}.

$$11x^{2}+30xy+25\left(x+3y\right)^{2}$$

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

$$11x^{2}+30xy+25\left(x^{2}+6xy+9y^{2}\right)$$

Use the distributive property to multiply 25 by x^{2}+6xy+9y^{2}.

$$11x^{2}+30xy+25x^{2}+150xy+225y^{2}$$

Combine 11x^{2} and 25x^{2} to get 36x^{2}.

$$36x^{2}+30xy+150xy+225y^{2}$$

Combine 30xy and 150xy to get 180xy.

$$36x^{2}+180xy+225y^{2}$$

Expand

$$36x^{2}+180xy+225y^{2}$$

Solution Steps

Use the distributive property to multiply 10x by x+3y.

$$x^{2}+10x^{2}+30xy+25\left(x+3y\right)^{2}$$

Combine x^{2} and 10x^{2} to get 11x^{2}.

$$11x^{2}+30xy+25\left(x+3y\right)^{2}$$

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

$$11x^{2}+30xy+25\left(x^{2}+6xy+9y^{2}\right)$$

Use the distributive property to multiply 25 by x^{2}+6xy+9y^{2}.

$$11x^{2}+30xy+25x^{2}+150xy+225y^{2}$$

Combine 11x^{2} and 25x^{2} to get 36x^{2}.

$$36x^{2}+30xy+150xy+225y^{2}$$

Combine 30xy and 150xy to get 180xy.

$$36x^{2}+180xy+225y^{2}$$