Solve 11(9-x)^2-(5-x)(5+x)-2x^2=

$$11 ( 9 - x ) ^ { 2 } - ( 5 - x ) ( 5 + x ) - 2 x ^ { 2 } =$$

Evaluate

$$10x^{2}-198x+866$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9-x\right)^{2}.

$$11\left(81-18x+x^{2}\right)-\left(5-x\right)\left(5+x\right)-2x^{2}$$

Use the distributive property to multiply 11 by 81-18x+x^{2}.

$$891-198x+11x^{2}-\left(5-x\right)\left(5+x\right)-2x^{2}$$

Consider \left(5-x\right)\left(5+x\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 5.

$$891-198x+11x^{2}-\left(25-x^{2}\right)-2x^{2}$$

To find the opposite of 25-x^{2}, find the opposite of each term.

$$891-198x+11x^{2}-25+x^{2}-2x^{2}$$

Subtract 25 from 891 to get 866.

$$866-198x+11x^{2}+x^{2}-2x^{2}$$

Combine 11x^{2} and x^{2} to get 12x^{2}.

$$866-198x+12x^{2}-2x^{2}$$

Combine 12x^{2} and -2x^{2} to get 10x^{2}.

$$866-198x+10x^{2}$$

Expand

$$10x^{2}-198x+866$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9-x\right)^{2}.

$$11\left(81-18x+x^{2}\right)-\left(5-x\right)\left(5+x\right)-2x^{2}$$

Use the distributive property to multiply 11 by 81-18x+x^{2}.

$$891-198x+11x^{2}-\left(5-x\right)\left(5+x\right)-2x^{2}$$

Consider \left(5-x\right)\left(5+x\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 5.

$$891-198x+11x^{2}-\left(25-x^{2}\right)-2x^{2}$$

To find the opposite of 25-x^{2}, find the opposite of each term.

$$891-198x+11x^{2}-25+x^{2}-2x^{2}$$

Subtract 25 from 891 to get 866.

$$866-198x+11x^{2}+x^{2}-2x^{2}$$

Combine 11x^{2} and x^{2} to get 12x^{2}.

$$866-198x+12x^{2}-2x^{2}$$

Combine 12x^{2} and -2x^{2} to get 10x^{2}.

$$866-198x+10x^{2}$$