Solve (x+8)(x-3)(x+3)(x-3)

$$( x + 8 ) ( x - 3 ) ( x + 3 ) ( x - 3 )$$

Evaluate

$$\left(x+3\right)\left(x+8\right)\left(x-3\right)^{2}$$

Solution Steps

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

$$\left(x+8\right)\left(x-3\right)^{2}\left(x+3\right)$$

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

$$\left(x+8\right)\left(x^{2}-6x+9\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of x+8 by each term of x^{2}-6x+9.

$$\left(x^{3}-6x^{2}+9x+8x^{2}-48x+72\right)\left(x+3\right)$$

Combine -6x^{2} and 8x^{2} to get 2x^{2}.

$$\left(x^{3}+2x^{2}+9x-48x+72\right)\left(x+3\right)$$

Combine 9x and -48x to get -39x.

$$\left(x^{3}+2x^{2}-39x+72\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of x^{3}+2x^{2}-39x+72 by each term of x+3.

$$x^{4}+3x^{3}+2x^{3}+6x^{2}-39x^{2}-117x+72x+216$$

Combine 3x^{3} and 2x^{3} to get 5x^{3}.

$$x^{4}+5x^{3}+6x^{2}-39x^{2}-117x+72x+216$$

Combine 6x^{2} and -39x^{2} to get -33x^{2}.

$$x^{4}+5x^{3}-33x^{2}-117x+72x+216$$

Combine -117x and 72x to get -45x.

$$x^{4}+5x^{3}-33x^{2}-45x+216$$

Expand

$$x^{4}+5x^{3}-33x^{2}-45x+216$$

Solution Steps

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

$$\left(x+8\right)\left(x-3\right)^{2}\left(x+3\right)$$

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

$$\left(x+8\right)\left(x^{2}-6x+9\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of x+8 by each term of x^{2}-6x+9.

$$\left(x^{3}-6x^{2}+9x+8x^{2}-48x+72\right)\left(x+3\right)$$

Combine -6x^{2} and 8x^{2} to get 2x^{2}.

$$\left(x^{3}+2x^{2}+9x-48x+72\right)\left(x+3\right)$$

Combine 9x and -48x to get -39x.

$$\left(x^{3}+2x^{2}-39x+72\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of x^{3}+2x^{2}-39x+72 by each term of x+3.

$$x^{4}+3x^{3}+2x^{3}+6x^{2}-39x^{2}-117x+72x+216$$

Combine 3x^{3} and 2x^{3} to get 5x^{3}.

$$x^{4}+5x^{3}+6x^{2}-39x^{2}-117x+72x+216$$

Combine 6x^{2} and -39x^{2} to get -33x^{2}.

$$x^{4}+5x^{3}-33x^{2}-117x+72x+216$$

Combine -117x and 72x to get -45x.

$$x^{4}+5x^{3}-33x^{2}-45x+216$$