Solve (x^2-5x)^2+10(x^2-5x)-15

$$( x ^ { 2 } - 5 x ) ^ { 2 } + 10 ( x ^ { 2 } - 5 x ) - 15$$

Evaluate

$$\left(x\left(x-5\right)\right)^{2}+10x\left(x-5\right)-15$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-10x^{2}x+25x^{2}+10\left(x^{2}-5x\right)-15$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-10x^{2}x+25x^{2}+10\left(x^{2}-5x\right)-15$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-10x^{3}+25x^{2}+10\left(x^{2}-5x\right)-15$$

Use the distributive property to multiply 10 by x^{2}-5x.

$$x^{4}-10x^{3}+25x^{2}+10x^{2}-50x-15$$

Combine 25x^{2} and 10x^{2} to get 35x^{2}.

$$x^{4}-10x^{3}+35x^{2}-50x-15$$

Expand

$$x^{4}-10x^{3}+35x^{2}-50x-15$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-10x^{2}x+25x^{2}+10\left(x^{2}-5x\right)-15$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-10x^{2}x+25x^{2}+10\left(x^{2}-5x\right)-15$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-10x^{3}+25x^{2}+10\left(x^{2}-5x\right)-15$$

Use the distributive property to multiply 10 by x^{2}-5x.

$$x^{4}-10x^{3}+25x^{2}+10x^{2}-50x-15$$

Combine 25x^{2} and 10x^{2} to get 35x^{2}.

$$x^{4}-10x^{3}+35x^{2}-50x-15$$