Question

find the product. simplify your answer.
(7x - 4)(x³ + 5x - 1)

Explanation:

Step1: Distribute \(7x\)

Multiply \(7x\) by each term in \((x^{3}+5x - 1)\):
\(7x\times x^{3}=7x^{4}\), \(7x\times5x = 35x^{2}\), \(7x\times(-1)=-7x\)

Step2: Distribute \(-4\)

Multiply \(-4\) by each term in \((x^{3}+5x - 1)\):
\(-4\times x^{3}=-4x^{3}\), \(-4\times5x=-20x\), \(-4\times(-1) = 4\)

Step3: Combine like terms

Combine the results from Step1 and Step2:
\(7x^{4}+35x^{2}-7x-4x^{3}-20x + 4\)
Combine the \(x\)-terms: \(-7x-20x=-27x\)

Step4: Write in standard form

Arrange terms in descending order of exponents:
\(7x^{4}-4x^{3}+35x^{2}-27x + 4\)

Answer:

\(7x^{4}-4x^{3}+35x^{2}-27x + 4\)