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

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

Evaluate

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

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of x+2 by each term of x-1.

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

Combine -x and 2x to get x.

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

To find the opposite of x^{2}+x-2, find the opposite of each term.

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

The opposite of -2 is 2.

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

Combine x^{2} and -x^{2} to get 0.

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

Expand

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

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of x+2 by each term of x-1.

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

Combine -x and 2x to get x.

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

To find the opposite of x^{2}+x-2, find the opposite of each term.

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

The opposite of -2 is 2.

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

Combine x^{2} and -x^{2} to get 0.

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