Solve 85(x+7)^2-(x-3)(x+3)=

$$85 ( x + 7 ) ^ { 2 } - ( x - 3 ) ( x + 3 ) =$$

Evaluate

$$84x^{2}+1190x+4174$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+7\right)^{2}.

$$85\left(x^{2}+14x+49\right)-\left(x-3\right)\left(x+3\right)$$

Use the distributive property to multiply 85 by x^{2}+14x+49.

$$85x^{2}+1190x+4165-\left(x-3\right)\left(x+3\right)$$

Consider \left(x-3\right)\left(x+3\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 3.

$$85x^{2}+1190x+4165-\left(x^{2}-9\right)$$

To find the opposite of x^{2}-9, find the opposite of each term.

$$85x^{2}+1190x+4165-x^{2}+9$$

Combine 85x^{2} and -x^{2} to get 84x^{2}.

$$84x^{2}+1190x+4165+9$$

Add 4165 and 9 to get 4174.

$$84x^{2}+1190x+4174$$

Expand

$$84x^{2}+1190x+4174$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+7\right)^{2}.

$$85\left(x^{2}+14x+49\right)-\left(x-3\right)\left(x+3\right)$$

Use the distributive property to multiply 85 by x^{2}+14x+49.

$$85x^{2}+1190x+4165-\left(x-3\right)\left(x+3\right)$$

Consider \left(x-3\right)\left(x+3\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 3.

$$85x^{2}+1190x+4165-\left(x^{2}-9\right)$$

To find the opposite of x^{2}-9, find the opposite of each term.

$$85x^{2}+1190x+4165-x^{2}+9$$

Combine 85x^{2} and -x^{2} to get 84x^{2}.

$$84x^{2}+1190x+4165+9$$

Add 4165 and 9 to get 4174.

$$84x^{2}+1190x+4174$$