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

$$( x + 2 y ) ( x - 2 y ) + ( x - y ) ( x + 2 )$$

Evaluate

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

Solution Steps

Consider \left(x+2y\right)\left(x-2y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(2y\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of x-y by each term of x+2.

$$x^{2}-4y^{2}+x^{2}+2x-yx-2y$$

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

$$2x^{2}-4y^{2}+2x-yx-2y$$

Expand

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

Solution Steps

Consider \left(x+2y\right)\left(x-2y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(2y\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of x-y by each term of x+2.

$$x^{2}-4y^{2}+x^{2}+2x-yx-2y$$

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

$$2x^{2}-4y^{2}+2x-yx-2y$$