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

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

Evaluate

$$-5x-7$$

Solution Steps

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

Use the distributive property to multiply -3 by x+2.

$$x^{2}-1-3x-6-x\left(x+2\right)$$

Subtract 6 from -1 to get -7.

$$x^{2}-7-3x-x\left(x+2\right)$$

Use the distributive property to multiply x by x+2.

$$x^{2}-7-3x-\left(x^{2}+2x\right)$$

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

$$x^{2}-7-3x-x^{2}-2x$$

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

$$-7-3x-2x$$

Combine -3x and -2x to get -5x.

$$-7-5x$$

Expand

$$-5x-7$$

Solution Steps

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

Use the distributive property to multiply -3 by x+2.

$$x^{2}-1-3x-6-x\left(x+2\right)$$

Subtract 6 from -1 to get -7.

$$x^{2}-7-3x-x\left(x+2\right)$$

Use the distributive property to multiply x by x+2.

$$x^{2}-7-3x-\left(x^{2}+2x\right)$$

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

$$x^{2}-7-3x-x^{2}-2x$$

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

$$-7-3x-2x$$

Combine -3x and -2x to get -5x.

$$-7-5x$$