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

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

Evaluate

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

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}.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

Use the distributive property to multiply x^{2}-2x-3 by x.

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

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

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

The opposite of -2x^{2} is 2x^{2}.

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

The opposite of -3x is 3x.

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

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

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

Expand

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

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}.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

Use the distributive property to multiply x^{2}-2x-3 by x.

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

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

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

The opposite of -2x^{2} is 2x^{2}.

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

The opposite of -3x is 3x.

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

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

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