Solve (x+6)(x-6)-(x-2)^2

$$( x + 6 ) ( x - 6 ) - ( x - 2 ) ^ { 2 }$$

Evaluate

$$4\left(x-10\right)$$

Solution Steps

Consider \left(x+6\right)\left(x-6\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 6.

$$x^{2}-36-\left(x-2\right)^{2}$$

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

$$x^{2}-36-\left(x^{2}-4x+4\right)$$

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

$$x^{2}-36-x^{2}+4x-4$$

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

$$-36+4x-4$$

Subtract 4 from -36 to get -40.

$$-40+4x$$

Expand

$$4x-40$$

Solution Steps

Consider \left(x+6\right)\left(x-6\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 6.

$$x^{2}-36-\left(x-2\right)^{2}$$

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

$$x^{2}-36-\left(x^{2}-4x+4\right)$$

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

$$x^{2}-36-x^{2}+4x-4$$

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

$$-36+4x-4$$

Subtract 4 from -36 to get -40.

$$-40+4x$$