Solve -x(x+3)^2(x-5)

$$- x ( x + 3 ) ^ { 2 } ( x - 5 )$$

Evaluate

$$-x\left(x-5\right)\left(x+3\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$\left(-x\right)\left(x^{2}+6x+9\right)\left(x-5\right)$$

Use the distributive property to multiply -x by x^{2}+6x+9.

$$\left(\left(-x\right)x^{2}+6\left(-x\right)x+9\left(-x\right)\right)\left(x-5\right)$$

Use the distributive property to multiply \left(-x\right)x^{2}+6\left(-x\right)x+9\left(-x\right) by x-5 and combine like terms.

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}-21\left(-x\right)x-45\left(-x\right)$$

Multiply -21 and -1 to get 21.

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}+21xx-45\left(-x\right)$$

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

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}+21x^{2}-45\left(-x\right)$$

Multiply -45 and -1 to get 45.

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}+21x^{2}+45x$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-x^{4}-xx^{2}+21x^{2}+45x$$

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

$$-x^{4}-x^{3}+21x^{2}+45x$$

Expand

$$45x+21x^{2}-x^{3}-x^{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$\left(-x\right)\left(x^{2}+6x+9\right)\left(x-5\right)$$

Use the distributive property to multiply -x by x^{2}+6x+9.

$$\left(\left(-x\right)x^{2}+6\left(-x\right)x+9\left(-x\right)\right)\left(x-5\right)$$

Use the distributive property to multiply \left(-x\right)x^{2}+6\left(-x\right)x+9\left(-x\right) by x-5 and combine like terms.

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}-21\left(-x\right)x-45\left(-x\right)$$

Multiply -21 and -1 to get 21.

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}+21xx-45\left(-x\right)$$

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

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}+21x^{2}-45\left(-x\right)$$

Multiply -45 and -1 to get 45.

$$\left(-x\right)x^{3}+\left(-x\right)x^{2}+21x^{2}+45x$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-x^{4}-xx^{2}+21x^{2}+45x$$

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

$$-x^{4}-x^{3}+21x^{2}+45x$$