Solve f(x)=6(x-8)(x+3)^3

$$f ( x ) = 6 ( x - 8 ) ( x + 3 ) ^ { 3 }$$

Evaluate

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

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}.

$$6\left(x-8\right)\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply 6 by x-8.

$$\left(6x-48\right)\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply 6x-48 by x^{3}+9x^{2}+27x+27 and combine like terms.

$$6x^{4}+6x^{3}-270x^{2}-1134x-1296$$

Expand

$$6x^{4}+6x^{3}-270x^{2}-1134x-1296$$

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}.

$$6\left(x-8\right)\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply 6 by x-8.

$$\left(6x-48\right)\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply 6x-48 by x^{3}+9x^{2}+27x+27 and combine like terms.

$$6x^{4}+6x^{3}-270x^{2}-1134x-1296$$