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Chapter 5: Problem 103

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

Short Answer

Expert verified
The multiplication of the binomials \( (x + 3) \) and \( (y - 2) \) using the FOIL method results in \( xy - 2x + 3y - 6 \).

Step by step solution

01

Identify the Binomials

To illustrate the FOIL method we will use the binomials \( (x + 3) \) and \( (y - 2) \).
02

Apply F of FOIL

First, we multiply the first terms of each binomial. In this case, that gives us \( x*y \) which is \( xy \).
03

Apply O of FOIL

Next, we multiply the outer terms of the binomials. In this case, that gives \( x*(-2) \) which is \( -2x \).
04

Apply I of FOIL

Now we multiply the inner terms of the binomials. In this case, that gives \( 3*y \) which is \( 3y \).
05

Apply L of FOIL

Finally, we multiply the last terms of the binomials. In this case, that gives \( 3*(-2) \) which is \( -6 \).
06

Combine All Terms

Combine all terms from the multiplication: \( xy - 2x + 3y - 6 \).

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Most popular questions from this chapter

Perform the indicated computations. Express answers in scientific notation. $$\frac{\left(1.2 \times 10^{6}\right)\left(8.7 \times 10^{-2}\right)}{\left(2.9 \times 10^{6}\right)\left(3 \times 10^{-3}\right)}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$5^{-2}>2^{-5}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I wrote a number where there is no advantage to using scientific notation instead of decimal notation.

In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{8 x^{6} y^{3}-12 x^{8} y^{2}-4 x^{14} y^{6}}{-4 x^{6} y^{2}}$$

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)-(y-1)\left(y^{2}+y+1\right)$$
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