Solve f(x)=7(x-5)(x+1)^3

$$f ( x ) = 7 ( x - 5 ) ( x + 1 ) ^ { 3 }$$

Evaluate

$$7\left(x-5\right)\left(x+1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

$$7\left(x-5\right)\left(x^{3}+3x^{2}+3x+1\right)$$

Use the distributive property to multiply 7 by x-5.

$$\left(7x-35\right)\left(x^{3}+3x^{2}+3x+1\right)$$

Use the distributive property to multiply 7x-35 by x^{3}+3x^{2}+3x+1 and combine like terms.

$$7x^{4}-14x^{3}-84x^{2}-98x-35$$

Expand

$$7x^{4}-14x^{3}-84x^{2}-98x-35$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

$$7\left(x-5\right)\left(x^{3}+3x^{2}+3x+1\right)$$

Use the distributive property to multiply 7 by x-5.

$$\left(7x-35\right)\left(x^{3}+3x^{2}+3x+1\right)$$

Use the distributive property to multiply 7x-35 by x^{3}+3x^{2}+3x+1 and combine like terms.

$$7x^{4}-14x^{3}-84x^{2}-98x-35$$