Solve 6(x-10)^2-(x+5)^2=

$$6 ( x - 10 ) ^ { 2 } - ( x + 5 ) ^ { 2 } =$$

Evaluate

$$5\left(x^{2}-26x+115\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-10\right)^{2}.

$$6\left(x^{2}-20x+100\right)-\left(x+5\right)^{2}$$

Use the distributive property to multiply 6 by x^{2}-20x+100.

$$6x^{2}-120x+600-\left(x+5\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$6x^{2}-120x+600-\left(x^{2}+10x+25\right)$$

To find the opposite of x^{2}+10x+25, find the opposite of each term.

$$6x^{2}-120x+600-x^{2}-10x-25$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}-120x+600-10x-25$$

Combine -120x and -10x to get -130x.

$$5x^{2}-130x+600-25$$

Subtract 25 from 600 to get 575.

$$5x^{2}-130x+575$$

Expand

$$5x^{2}-130x+575$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-10\right)^{2}.

$$6\left(x^{2}-20x+100\right)-\left(x+5\right)^{2}$$

Use the distributive property to multiply 6 by x^{2}-20x+100.

$$6x^{2}-120x+600-\left(x+5\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$6x^{2}-120x+600-\left(x^{2}+10x+25\right)$$

To find the opposite of x^{2}+10x+25, find the opposite of each term.

$$6x^{2}-120x+600-x^{2}-10x-25$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}-120x+600-10x-25$$

Combine -120x and -10x to get -130x.

$$5x^{2}-130x+600-25$$

Subtract 25 from 600 to get 575.

$$5x^{2}-130x+575$$