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

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

Evaluate

$$8\left(x-y\right)\left(4y-x\right)$$

Solution Steps

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

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

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

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

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

$$x^{2}+4xy+4y^{2}-9x^{2}+36xy-36y^{2}$$

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

$$-8x^{2}+4xy+4y^{2}+36xy-36y^{2}$$

Combine 4xy and 36xy to get 40xy.

$$-8x^{2}+40xy+4y^{2}-36y^{2}$$

Combine 4y^{2} and -36y^{2} to get -32y^{2}.

$$-8x^{2}+40xy-32y^{2}$$

Expand

$$-8x^{2}+40xy-32y^{2}$$

Solution Steps

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

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

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

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

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

$$x^{2}+4xy+4y^{2}-9x^{2}+36xy-36y^{2}$$

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

$$-8x^{2}+4xy+4y^{2}+36xy-36y^{2}$$

Combine 4xy and 36xy to get 40xy.

$$-8x^{2}+40xy+4y^{2}-36y^{2}$$

Combine 4y^{2} and -36y^{2} to get -32y^{2}.

$$-8x^{2}+40xy-32y^{2}$$