Solve (x + 3) ^ 2 - (x - 3) ^ 2 * (x + 3) = | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(x+3)^{2}-(x-3)^{2}\cdot(x+3)=$$

Evaluate

$\left(1-x\right)\left(x-6\right)\left(x+3\right)$

Solution Steps

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

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

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

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

Use the distributive property to multiply $x^{2}-6x+9$ by $x+3$ and combine like terms.

$$x^{2}+6x+9-\left(x^{3}-3x^{2}-9x+27\right)$$

To find the opposite of $x^{3}-3x^{2}-9x+27$, find the opposite of each term.

$$x^{2}+6x+9-x^{3}+3x^{2}+9x-27$$

Combine $x^{2}$ and $3x^{2}$ to get $4x^{2}$.

$$4x^{2}+6x+9-x^{3}+9x-27$$

Combine $6x$ and $9x$ to get $15x$.

$$4x^{2}+15x+9-x^{3}-27$$

Subtract $27$ from $9$ to get $-18$.

$$4x^{2}+15x-18-x^{3}$$

Expand

$-x^{3}+4x^{2}+15x-18$

Solution Steps

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

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

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

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

Use the distributive property to multiply $x^{2}-6x+9$ by $x+3$ and combine like terms.

$$x^{2}+6x+9-\left(x^{3}-3x^{2}-9x+27\right)$$

To find the opposite of $x^{3}-3x^{2}-9x+27$, find the opposite of each term.

$$x^{2}+6x+9-x^{3}+3x^{2}+9x-27$$

Combine $x^{2}$ and $3x^{2}$ to get $4x^{2}$.

$$4x^{2}+6x+9-x^{3}+9x-27$$

Combine $6x$ and $9x$ to get $15x$.

$$4x^{2}+15x+9-x^{3}-27$$

Subtract $27$ from $9$ to get $-18$.

$$4x^{2}+15x-18-x^{3}$$