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Chapter 6: Problem 1

Use FOIL to find the products in Exercises 1-8. \((x+3)(x+5)\)

Short Answer

Expert verified
The product of \((x+3)(x+5)\) using the FOIL method is \(x^2 + 8x + 15\).

Step by step solution

01

First: Multiply the first terms

Take \(x\) from \((x+3)\) and \(x\) from \((x+5)\) and multiply them: \(x \cdot x = x^2\). So, our first term is \(x^2\).
02

Outside: Multiply the outside terms

Take \(x\) from \((x+3)\) and \(5\) from \((x+5)\) and multiply them: \(x \cdot 5 = 5x\). So, our outside term is \(5x\).
03

Inside: Multiply the inside terms

Take \(3\) from \((x+3)\) and \(x\) from \((x+5)\) and multiply them: \(3 \cdot x = 3x\). So, our inside term is \(3x\).
04

Last: Multiply the last terms

Take \(3\) from \((x+3)\) and \(5\) from \((x+5)\) and multiply them: \(3 \cdot 5 = 15\). So, our last term is 15.
05

Combine all terms

Now, combine all the terms obtained from the FOIL process: \(x^2 + 5x + 3x + 15\). Combine the like terms to simplify: \(x^2 + 8x + 15\).

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-x-2\)

Factor the trinomials in Exercises 9-32, or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+5 x+6\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x-36\)

Solve the equations using the quadratic formula. \(9 x^{2}+6 x+1=0\)

Solve the quadratic equations in Exercises \(37-52\) by factoring. \(x^{2}+8 x+15=0\)
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