Solve (x+2)(x-2)-(x-1)(x+5)

$$(x+2)(x-2)-(x-1)(x+5)$$

Evaluate

$$1-4x$$

Solution Steps

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

$$x^{2}-2^{2}-\left(x-1\right)\left(x+5\right)$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}-4-\left(x-1\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x-1 by each term of x+5.

$$x^{2}-4-\left(x^{2}+5x-x-5\right)$$

Combine 5x and -x to get 4x.

$$x^{2}-4-\left(x^{2}+4x-5\right)$$

To find the opposite of x^{2}+4x-5, find the opposite of each term.

$$x^{2}-4-x^{2}-4x-\left(-5\right)$$

The opposite of -5 is 5.

$$x^{2}-4-x^{2}-4x+5$$

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

$$-4-4x+5$$

Add -4 and 5 to get 1.

$$1-4x$$

Expand

$$1-4x$$

Solution Steps

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

$$x^{2}-2^{2}-\left(x-1\right)\left(x+5\right)$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}-4-\left(x-1\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x-1 by each term of x+5.

$$x^{2}-4-\left(x^{2}+5x-x-5\right)$$

Combine 5x and -x to get 4x.

$$x^{2}-4-\left(x^{2}+4x-5\right)$$

To find the opposite of x^{2}+4x-5, find the opposite of each term.

$$x^{2}-4-x^{2}-4x-\left(-5\right)$$

The opposite of -5 is 5.

$$x^{2}-4-x^{2}-4x+5$$

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

$$-4-4x+5$$

Add -4 and 5 to get 1.

$$1-4x$$