Problem 69 Factor. $$ 8 x+6 y $$... [FREE SOLUTION]

Chapter 15: Problem 69

Factor. $$ 8 x+6 y $$

Short Answer

Expert verified

2(4x + 3y)

Step by step solution

Identify the Common Factor

First, look at the coefficients of the terms in the expression. The terms are 8 and 6. Find the greatest common factor (GCF) of these numbers. The GCF of 8 and 6 is 2.

Factor Out the GCF

Next, factor the GCF out of each term. Divide each term by the GCF and place the remaining expression inside parentheses. For the first term: $ \frac{8x}{2} = 4x $ For the second term: $ \frac{6y}{2} = 3y $

Write the Factorized Expression

Combine the common factor and the terms from which it was factored out. The expression becomes 2(4x + 3y).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Greatest Common Factor

The Greatest Common Factor (GCF) is the largest number that can divide evenly into two or more given numbers. It's essential when factoring algebraic expressions as it simplifies the problem.
For example, in the expression $8x + 6y$, the coefficients are 8 and 6. To find the GCF, we need to find the largest number that divides both 8 and 6 without leaving a remainder.
Start by listing the factors of each number:
- Factors of 8: 1, 2, 4, 8
- Factors of 6: 1, 2, 3, 6
The highest common factor in these lists is 2, which means 2 is our GCF for the coefficients 8 and 6.

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables (like x or y), and operators (such as + or -). In our exercise, we have the expression $8x + 6y$.
Let's break down the components:
- 8x: Here, 8 is the coefficient (a constant number), and x is the variable.
- 6y: Similarly, 6 is the coefficient, and y is the variable.
Algebraic expressions can be simplified or factored by looking for common factors among their terms.
In our example, we factor by finding the GCF, which simplifies the expression to a more manageable form.

Factoring Techniques

Factoring is the process of breaking down an expression into multiples that can be multiplied together to get the original expression.
Let's focus on the standard technique used in our example:
1. Identify the GCF: From the terms 8x and 6y, the GCF is 2.
2. Factor Out the GCF: Dividing each term by 2, we get $ \frac{8x}{2} = 4x $ and $ \frac{6y}{2} = 3y $.
3. Rewrite the Expression: Combine the GCF with the simplified terms to get the factored form $ 2(4x + 3y) $.

By following these steps, you can factor almost any algebraic expression efficiently. Remember, it's all about identifying the common factors and simplifying where possible.

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91影视

Factor. $$ 8 x+6 y $$

Short Answer

Step by step solution

Identify the Common Factor

Factor Out the GCF

Write the Factorized Expression

Key Concepts

Greatest Common Factor

Algebraic Expressions

Factoring Techniques

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