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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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