Solve (x+2)(x-2)-(x+1)(x-3)

$$( x + 2 ) ( x - 2 ) - ( x + 1 ) ( x - 3 )$$

Evaluate

$$2x-1$$

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}.

$$x^{2}-2^{2}-\left(x+1\right)\left(x-3\right)$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}-4-\left(x+1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x+1 by each term of x-3.

$$x^{2}-4-\left(x^{2}-3x+x-3\right)$$

Combine -3x and x to get -2x.

$$x^{2}-4-\left(x^{2}-2x-3\right)$$

To find the opposite of x^{2}-2x-3, find the opposite of each term.

$$x^{2}-4-x^{2}-\left(-2x\right)-\left(-3\right)$$

The opposite of -2x is 2x.

$$x^{2}-4-x^{2}+2x-\left(-3\right)$$

The opposite of -3 is 3.

$$x^{2}-4-x^{2}+2x+3$$

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

$$-4+2x+3$$

Add -4 and 3 to get -1.

$$-1+2x$$

Expand

$$2x-1$$

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}.

$$x^{2}-2^{2}-\left(x+1\right)\left(x-3\right)$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}-4-\left(x+1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x+1 by each term of x-3.

$$x^{2}-4-\left(x^{2}-3x+x-3\right)$$

Combine -3x and x to get -2x.

$$x^{2}-4-\left(x^{2}-2x-3\right)$$

To find the opposite of x^{2}-2x-3, find the opposite of each term.

$$x^{2}-4-x^{2}-\left(-2x\right)-\left(-3\right)$$

The opposite of -2x is 2x.

$$x^{2}-4-x^{2}+2x-\left(-3\right)$$

The opposite of -3 is 3.

$$x^{2}-4-x^{2}+2x+3$$

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

$$-4+2x+3$$

Add -4 and 3 to get -1.

$$-1+2x$$