Question

Simplify each expression. If an expression cannot be simplified, so state. $2 a^{2}-4 a b+5 a b-10 b^{2}$

Name: Problem 40, Chapter 2: Intermediate Algebra for College Students
Uploaded: 2020-05-03T16:53:22-08:00
Duration: 1 min 46 s
Channel: Peggy Radtke
Description: Simplify each expression. If an expression cannot be simplified, so state. 2 a^2-4 a b+5 a b-10 b^2

   Simplify each expression. If an expression cannot be simplified, so state. $2 a^{2}-4 a b+5 a b-10 b^{2}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 2, Problem 40

Instant Answer

Solved by Expert Peggy Radtke

05/03/2020

Step 1

First, we can combine the like terms, which are the terms with $ab$: $2a^2 - 4ab + 5ab - 10b^2 = 2a^2 + (5 - 4)ab - 10b^2$ Now, we have: Show more…

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Simplify each expression. If an expression cannot be simplified, so state. $2 a^{2}-4 a b+5 a b-10 b^{2}$

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Key Concepts

Polynomial Simplification

Simplifying a polynomial means rewriting it in a reduced form by combining like terms and, if possible, factoring common elements. It makes the expression clearer and sets the stage for further operations like factoring, solving equations, or further algebraic manipulations.

Combining Like Terms

This process involves identifying terms in an expression that have the exact same variables raised to the same powers and then adding or subtracting their coefficients. In the context of simplifying polynomial expressions, it is a vital first step that reduces the expression to a more manageable and more easily interpretable form.

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