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Chapter 10: Problem 35

Factor out the greatest common factor. $$5 m+40 n$$

Short Answer

Expert verified
5(m + 8n)

Step by step solution

01

Identify the Greatest Common Factor (GCF)

List the factors of each term in the expression. For 5m, the factors are 1, 5, m. For 40n, the factors are 1, 2, 4, 5, 8, 10, 20, 40, n. The common factor is 5.
02

Factor Out the GCF

Express each term as a product of the GCF and another factor. Break down 5m as 5 * m and 40n as 5 * 8n. The expression becomes 5(m) + 5(8n).
03

Rewrite the Expression

Factor out the GCF, 5, from each term. The expression becomes 5(m + 8n).

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Key Concepts

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

prealgebra
Prealgebra serves as the foundation for more complicated math like algebra and calculus. In prealgebra, we deal with basic arithmetic, simple equations, and basic number theory.
Mastering these basic skills is essential for understanding more advanced mathematical concepts.
This initial stage covers understanding integers, fractions, and the relationships between numbers.
factoring
Factoring involves breaking down a number or an expression into simpler elements called factors.
For example, when we factorize the expression \(5m + 40n\), we look for common factors in both terms.
This simplification helps in solving equations and makes other calculations easier.
greatest common factor
The Greatest Common Factor (GCF) is the largest factor that two or more numbers have in common.
To find it, list every factor of each term and identify the highest factor that appears in both lists.
In the expression \(5m + 40n\), the GCF is 5 because it is the only number that evenly divides both 5 and 40.
This step is crucial because factoring out the GCF simplifies the expression, making it easier to work with.
mathematical expressions
A mathematical expression is a combination of numbers, variables (like \(m\) and \(n\)), and operators (like \(+\) and \(-\)).
Expressions do not have an equals sign; that鈥檚 what makes them different from equations.
Simplifying expressions by factoring helps in solving equations more efficiently and understanding relationships between different terms.
For instance, in the expression \(5m + 40n\), factoring out the GCF results in a simplified form, \(5(m + 8n)\), which is easier to handle.

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Most popular questions from this chapter

Simplify. $$\left(\frac{3}{4}\right)^{3}\left(\frac{3}{4}\right)^{4}$$

Simplify the expression. $$\left(y^{2}\right)^{3}\left(y^{4}\right)^{2}$$

Simplify. Write the answers with positive exponents only. $$\left(x y^{-4}\right)^{3}$$

Perform the indicated operations. $$\left(-9 m^{4}-7 m^{2}+8\right)-\left(3 m^{4}+9 m^{3}-11\right)-\left(8 m^{3}+m^{2}-3\right)$$

Subtract the polynomials. $$\left(-8 y^{4}+2 y^{2}-3 y+10\right)-\left(6 y^{4}+y^{3}+11 y-9\right)$$
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