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

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

Evaluate

$$4y-1$$

Solution Steps

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

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

Combine -4xy and 4yx to get 0.

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

Combine 2x and -2x to get 0.

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

Combine 2y and 2y to get 4y.

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

Consider \left(2x-2y\right)\left(2x+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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

To find the opposite of 4x^{2}-4y^{2}, find the opposite of each term.

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

The opposite of -4y^{2} is 4y^{2}.

$$4x^{2}-4y^{2}+4y-1-4x^{2}+4y^{2}$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-4y^{2}+4y-1+4y^{2}$$

Combine -4y^{2} and 4y^{2} to get 0.

$$4y-1$$

Expand

$$4y-1$$

Solution Steps

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

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

Combine -4xy and 4yx to get 0.

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

Combine 2x and -2x to get 0.

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

Combine 2y and 2y to get 4y.

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

Consider \left(2x-2y\right)\left(2x+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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

To find the opposite of 4x^{2}-4y^{2}, find the opposite of each term.

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

The opposite of -4y^{2} is 4y^{2}.

$$4x^{2}-4y^{2}+4y-1-4x^{2}+4y^{2}$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-4y^{2}+4y-1+4y^{2}$$

Combine -4y^{2} and 4y^{2} to get 0.

$$4y-1$$