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

$$( x + 1 ) ( x - 1 ) - ( x + 2 ) ^ { 2 }$$

Evaluate

$$-4x-5$$

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}. Square 1.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

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

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

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

$$-1-4x-4$$

Subtract 4 from -1 to get -5.

$$-5-4x$$

Expand

$$-4x-5$$

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}. Square 1.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

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

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

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

$$-1-4x-4$$

Subtract 4 from -1 to get -5.

$$-5-4x$$