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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Combine x^{3} and -x^{3} to get 0.

$$9x^{2}+27x+27+27$$

Add 27 and 27 to get 54.

$$9x^{2}+27x+54$$

Expand

$$9x^{2}+27x+54$$

Solution Steps

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

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

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

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

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

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

Combine x^{3} and -x^{3} to get 0.

$$9x^{2}+27x+27+27$$

Add 27 and 27 to get 54.

$$9x^{2}+27x+54$$