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Chapter 6: Problem 88

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

Short Answer

Expert verified
The product of two binomials, say \( (x + 3)(x + 2) \), using the FOIL method is \( x^2 + 5x + 6 \).

Step by step solution

01

First terms

To begin with, multiply the first terms in each binomial. Consider the example \( (x + 3)(x + 2) \). Here the first terms in each binomial are 'x' and 'x', giving you \( x \times x = x^2 \). This derives from the 'first' in FOIL.
02

Outer terms

Next, multiply the outer or the terms on the ends. In the example \( (x + 3)(x + 2) \), 'x' from the first binomial and '2' from the second binomial are the outer terms, so you have \( x \times 2 = 2x \). This comes from the 'outer' in FOIL.
03

Inner terms

Then, multiply the inner terms or those next to each other. In the example \( (x + 3)(x + 2) \), '3' from the first binomial and 'x' from the second binomial are inner terms, so you have \( 3 \times x = 3x \). This represents the 'inner' in FOIL.
04

Last terms

Finally, multiply the last terms in each binomial. In the example \( (x + 3)(x + 2) \), the last terms are '3' and '2', giving you \( 3 \times 2 = 6 \). This refers to the 'last' in FOIL.
05

Combine like terms

After multiplying, combine any like terms. In this case, \( 2x \) and \( 3x \) are like terms, and can be combined to make \( 5x \), so the final answer is \( x^2 + 5x + 6 \).

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Most popular questions from this chapter

In Exercises 73-80, solve each equation by the method of your choice. \(\frac{3 x^{2}}{4}-\frac{5 x}{2}-2=0\)

Use FOIL to find the products. \((2 x-5)(x+3)\)

Solve each equation by the method of your choice. \((2 x-6)(x+2)=5(x-1)-12\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(6 x^{2}-17 x+12\)

Solve each equation using the zero-product principle. \((4 x+5)(x-2)=0\)
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