Solving and Expanding Binomials Using the Distributive Property and FOIL Method

In this article, we will delve into the process of solving and expanding a specific binomial expression using the distributive property and the FOIL method. We will walk through each step to fully understand the algebraic operations involved. By the end of this article, you will be able to confidently solve similar problems on your own.

The Problem and the Method

We are given the expression:

6x 17 ( 6x - 13 )

This expression represents the expansion of a product of two binomials using the distributive property. The FOIL method, which stands for First, Outer, Inner, Last, can be used as a mnemonic to remember the order of multiplication.

Step-by-Step Solution

Let's break down the process of solving and expanding this binomial expression step by step.

First

Multiply the first terms in each binomial:

6x ? 6x 36x^2

Outer

Multiply the outer terms (first term in the first binomial and second term in the second binomial):

6x ? - 13 - 78x

Inner

Multiply the inner terms (second term in the first binomial and first term in the second binomial):

17 ? 6x 102x

Last

Multiply the last terms in each binomial:

17 ? - 13 - 221

Combining the Results

Now, combine all the results obtained from the previous steps:

36x^2 - 78x 102x - 221

Then, combine the like terms (the terms containing 6x ):

36x^2 - 78x 102x - 221 36x^2 - 78x 102x - 221 36x^2 24x - 221

The final expanded form of the expression is:

36x^2 24x - 221

Conclusion and Additional Tips

Solving and expanding binomials using the distributive property and FOIL method is a fundamental skill in algebra. By familiarizing yourself with the steps outlined in this article, you can confidently solve similar problems and deepen your understanding of polynomial multiplication.

Remember, practice is key to mastering these algebraic techniques. Use your newfound knowledge to tackle more complex expressions and equations, and you'll be well on your way to becoming an expert in algebra.

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