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

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

Evaluate

$\left(x^{2}-4\right)\left(x+3\right)^{2}$

Solution Steps

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

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

Use the distributive property to multiply $x-2$ by $x+2$ and combine like terms.

$$\left(x^{2}-4\right)\left(x^{2}+6x+9\right)$$

Use the distributive property to multiply $x^{2}-4$ by $x^{2}+6x+9$ and combine like terms.

$$x^{4}+6x^{3}+5x^{2}-24x-36$$

Expand

$x^{4}+6x^{3}+5x^{2}-24x-36$

Solution Steps

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

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

Use the distributive property to multiply $x-2$ by $x+2$ and combine like terms.

$$\left(x^{2}-4\right)\left(x^{2}+6x+9\right)$$

Use the distributive property to multiply $x^{2}-4$ by $x^{2}+6x+9$ and combine like terms.

$$x^{4}+6x^{3}+5x^{2}-24x-36$$