Solve x^3-9x+xleft(x+3right)^2+(-x^2(x+3))

$${ x }^{ 3 } -9x+x { \left(x+3 \right) }^{ 2 } +(- { x }^{ 2 } (x+3))$$

Evaluate

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

Solution Steps

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

$$x^{3}-9x+x\left(x^{2}+6x+9\right)+\left(-x^{2}\right)\left(x+3\right)$$

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

$$x^{3}-9x+x^{3}+6x^{2}+9x+\left(-x^{2}\right)\left(x+3\right)$$

Combine x^{3} and x^{3} to get 2x^{3}.

$$2x^{3}-9x+6x^{2}+9x+\left(-x^{2}\right)\left(x+3\right)$$

Combine -9x and 9x to get 0.

$$2x^{3}+6x^{2}+\left(-x^{2}\right)\left(x+3\right)$$

Use the distributive property to multiply -x^{2} by x+3.

$$2x^{3}+6x^{2}+\left(-x^{2}\right)x+3\left(-x^{2}\right)$$

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

$$2x^{3}+6x^{2}-x^{3}+3\left(-1\right)x^{2}$$

Combine 2x^{3} and -x^{3} to get x^{3}.

$$x^{3}+6x^{2}+3\left(-1\right)x^{2}$$

Multiply 3 and -1 to get -3.

$$x^{3}+6x^{2}-3x^{2}$$

Combine 6x^{2} and -3x^{2} to get 3x^{2}.

$$x^{3}+3x^{2}$$

Expand

$$x^{3}+3x^{2}$$

Solution Steps

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

$$x^{3}-9x+x\left(x^{2}+6x+9\right)+\left(-x^{2}\right)\left(x+3\right)$$

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

$$x^{3}-9x+x^{3}+6x^{2}+9x+\left(-x^{2}\right)\left(x+3\right)$$

Combine x^{3} and x^{3} to get 2x^{3}.

$$2x^{3}-9x+6x^{2}+9x+\left(-x^{2}\right)\left(x+3\right)$$

Combine -9x and 9x to get 0.

$$2x^{3}+6x^{2}+\left(-x^{2}\right)\left(x+3\right)$$

Use the distributive property to multiply -x^{2} by x+3.

$$2x^{3}+6x^{2}+\left(-x^{2}\right)x+3\left(-x^{2}\right)$$

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

$$2x^{3}+6x^{2}-x^{3}+3\left(-1\right)x^{2}$$

Combine 2x^{3} and -x^{3} to get x^{3}.

$$x^{3}+6x^{2}+3\left(-1\right)x^{2}$$

Multiply 3 and -1 to get -3.

$$x^{3}+6x^{2}-3x^{2}$$

Combine 6x^{2} and -3x^{2} to get 3x^{2}.

$$x^{3}+3x^{2}$$