# Algebra Question(Part of a Larger Problem)

• undrcvrbro
In summary, the conversation is about a request for help in simplifying the expression f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2). The back of the book provides the solution of 5x(x-5)^(2)(x-2). The person seeking help was advised to factor out the common term of x*(x-5)^2 which would leave 2(x-5) + (3x+1). After realizing their mistake, they were able to solve the problem.
undrcvrbro

## Homework Statement

f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2)

Need to simplify.

## The Attempt at a Solution

I tried simplifying completely but my answer wasn't even close. The Back of the book has:
5x(x-5)^(2)(x-2)

I know its easy, but I'm drawing a blank...can anyone start me off on the right path to find how they got that answer?

The first thing to notice is that both terms in your expression have a common factor of x*(x-5)^2. Factor that out. Now what's left in each term?

Well, wouldn't it then be 2(x-5) + (3x+1)?

I get just 2(x-5)+3x. Where did the 1 come from?

Oh! I got it!

Oh wow. I can't believe I had made a mistake like that. Thank you so much. I just figured it out.

Thanks Dick.

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Algebra is a branch of mathematics that helps us solve problems involving unknown values. It allows us to represent relationships between quantities using symbols and equations, making it a powerful tool in problem-solving.

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Algebra can be used to solve a variety of real-world problems, such as calculating distances, finding unknown measurements, and predicting future values. It is also used in fields such as finance, engineering, and science to analyze and model data.

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The basic concepts of algebra include variables, constants, expressions, equations, and inequalities. Variables are represented by letters and can take on different values. Constants are values that do not change. Expressions are combinations of variables, constants, and mathematical operations. Equations and inequalities are statements that show the equality or inequality between two expressions.

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## 5. Can algebra be challenging for some people?

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