Question

1. use the foil method to find the product. (v - 3)(v² + 8v)

Explanation:

Step1: Recall FOIL for binomialtrinomial? Wait, no, actually, FOIL is for binomialbinomial, but here we can distribute each term. Wait, first, let's treat \((v - 3)\) as a binomial and \((v^2 + 8v)\) as a binomial? Wait, no, \((v^2 + 8v)\) is a binomial (two terms). So FOIL: First, Outer, Inner, Last. Wait, actually, when multiplying two binomials \((a + b)(c + d)=ac + ad + bc + bd\). So here, \(a = v\), \(b=-3\), \(c = v^2\), \(d = 8v\).

Step1: Multiply First terms: \(v \times v^2\)

\(v \times v^2 = v^{1 + 2}=v^3\)

Step2: Multiply Outer terms: \(v \times 8v\)

\(v \times 8v = 8v^{1+1}=8v^2\)

Step3: Multiply Inner terms: \(-3 \times v^2\)

\(-3 \times v^2=-3v^2\)

Step4: Multiply Last terms: \(-3 \times 8v\)

\(-3 \times 8v=-24v\)

Step5: Combine like terms (the \(8v^2\) and \(-3v^2\))

\(v^3 + 8v^2 - 3v^2 - 24v = v^3 + (8 - 3)v^2 - 24v = v^3 + 5v^2 - 24v\)

Answer:

\(v^3 + 5v^2 - 24v\)