Solve [(-5+x)(-x-5)]^2

$$[ ( - 5 + x ) ( - x - 5 ) ] ^ { 2 }$$

Evaluate

$$\left(25-x^{2}\right)^{2}$$

Solution Steps

Use the distributive property to multiply -5+x by -x-5.

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

Multiply -5 and -1 to get 5.

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

Combine 5x and -5x to get 0.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(25+x\left(-x\right)\right)^{2}.

$$625+50x\left(-x\right)+x^{2}\left(-x\right)^{2}$$

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

$$625+50x\left(-x\right)+x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$625+50x\left(-x\right)+x^{4}$$

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

$$625+50x^{2}\left(-1\right)+x^{4}$$

Multiply 50 and -1 to get -50.

$$625-50x^{2}+x^{4}$$

Expand

$$x^{4}-50x^{2}+625$$

Solution Steps

Use the distributive property to multiply -5+x by -x-5.

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

Multiply -5 and -1 to get 5.

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

Combine 5x and -5x to get 0.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(25+x\left(-x\right)\right)^{2}.

$$625+50x\left(-x\right)+x^{2}\left(-x\right)^{2}$$

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

$$625+50x\left(-x\right)+x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$625+50x\left(-x\right)+x^{4}$$

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

$$625+50x^{2}\left(-1\right)+x^{4}$$

Multiply 50 and -1 to get -50.

$$625-50x^{2}+x^{4}$$