Solve (-X-5)^2-(5x-2)^2

$$( - X - 5 ) ^ { 2 } - ( 5 x - 2 ) ^ { 2 }$$

Evaluate

$$\left(7+X-5x\right)\left(5x+X+3\right)$$

Solution Steps

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

$$\left(-X\right)^{2}-10\left(-X\right)+25-\left(5x-2\right)^{2}$$

Calculate -X to the power of 2 and get X^{2}.

$$X^{2}-10\left(-X\right)+25-\left(5x-2\right)^{2}$$

Multiply -10 and -1 to get 10.

$$X^{2}+10X+25-\left(5x-2\right)^{2}$$

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

$$X^{2}+10X+25-\left(25x^{2}-20x+4\right)$$

To find the opposite of 25x^{2}-20x+4, find the opposite of each term.

$$X^{2}+10X+25-25x^{2}+20x-4$$

Subtract 4 from 25 to get 21.

$$X^{2}+10X+21-25x^{2}+20x$$

Expand

$$21+10X+X^{2}+20x-25x^{2}$$

Solution Steps

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

$$\left(-X\right)^{2}-10\left(-X\right)+25-\left(5x-2\right)^{2}$$

Calculate -X to the power of 2 and get X^{2}.

$$X^{2}-10\left(-X\right)+25-\left(5x-2\right)^{2}$$

Multiply -10 and -1 to get 10.

$$X^{2}+10X+25-\left(5x-2\right)^{2}$$

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

$$X^{2}+10X+25-\left(25x^{2}-20x+4\right)$$

To find the opposite of 25x^{2}-20x+4, find the opposite of each term.

$$X^{2}+10X+25-25x^{2}+20x-4$$

Subtract 4 from 25 to get 21.

$$X^{2}+10X+21-25x^{2}+20x$$