Solve (2)(x+2y)(x-2y)+(x+1)(x-1)

$$( 2 ) ( x + 2 y ) ( x - 2 y ) + ( x + 1 ) ( x - 1 )$$

Evaluate

$$3x^{2}-8y^{2}-1$$

Solution Steps

Use the distributive property to multiply 2 by x+2y.

$$\left(2x+4y\right)\left(x-2y\right)+\left(x+1\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of 2x+4y by each term of x-2y.

$$2x^{2}-4xy+4yx-8y^{2}+\left(x+1\right)\left(x-1\right)$$

Combine -4xy and 4yx to get 0.

$$2x^{2}-8y^{2}+\left(x+1\right)\left(x-1\right)$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$2x^{2}-8y^{2}+x^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$2x^{2}-8y^{2}+x^{2}-1$$

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}-8y^{2}-1$$

Expand

$$3x^{2}-8y^{2}-1$$

Solution Steps

Use the distributive property to multiply 2 by x+2y.

$$\left(2x+4y\right)\left(x-2y\right)+\left(x+1\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of 2x+4y by each term of x-2y.

$$2x^{2}-4xy+4yx-8y^{2}+\left(x+1\right)\left(x-1\right)$$

Combine -4xy and 4yx to get 0.

$$2x^{2}-8y^{2}+\left(x+1\right)\left(x-1\right)$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$2x^{2}-8y^{2}+x^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$2x^{2}-8y^{2}+x^{2}-1$$

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}-8y^{2}-1$$