Solve {l}{(x-7)(x+7)}{quad+(x-5)(x-1)}

$$\left. \begin{array} { l } { ( x - 7 ) ( x + 7 ) } \\ { \quad + ( x - 5 ) ( x - 1 ) } \end{array} \right.$$

Evaluate

$$2\left(x^{2}-3x-22\right)$$

Solution Steps

Consider \left(x-7\right)\left(x+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-7^{2}+\left(x-5\right)\left(x-1\right)$$

Calculate 7 to the power of 2 and get 49.

$$x^{2}-49+\left(x-5\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x-5 by each term of x-1.

$$x^{2}-49+x^{2}-x-5x+5$$

Combine -x and -5x to get -6x.

$$x^{2}-49+x^{2}-6x+5$$

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

$$2x^{2}-49-6x+5$$

Add -49 and 5 to get -44.

$$2x^{2}-44-6x$$

Expand

$$2x^{2}-6x-44$$

Solution Steps

Consider \left(x-7\right)\left(x+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-7^{2}+\left(x-5\right)\left(x-1\right)$$

Calculate 7 to the power of 2 and get 49.

$$x^{2}-49+\left(x-5\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x-5 by each term of x-1.

$$x^{2}-49+x^{2}-x-5x+5$$

Combine -x and -5x to get -6x.

$$x^{2}-49+x^{2}-6x+5$$

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

$$2x^{2}-49-6x+5$$

Add -49 and 5 to get -44.

$$2x^{2}-44-6x$$