Solve 9(x+y)^2-x^2

$$9 ( x + y ) ^ { 2 } - x ^ { 2 }$$

Evaluate

$$\left(2x+3y\right)\left(4x+3y\right)$$

Solution Steps

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

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

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

$$9x^{2}+18xy+9y^{2}-x^{2}$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}+18xy+9y^{2}$$

Expand

$$8x^{2}+18xy+9y^{2}$$

Solution Steps

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

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

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

$$9x^{2}+18xy+9y^{2}-x^{2}$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}+18xy+9y^{2}$$