Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem R.2.135

Chapter 1, Problem R.2.135

Simplify each expression. See Example 8. -12y + 4y + 3y + 2y

Verified step by step guidance

Identify the like terms in the expression: all terms contain the variable \(y\), so they can be combined.

Write the expression grouping the coefficients of \(y\): \(-12y + 4y + 3y + 2y\).

Add the coefficients together: calculate \(-12 + 4 + 3 + 2\).

Combine the sum of the coefficients with the variable \(y\) to form the simplified expression.

Write the final simplified expression as the product of the combined coefficient and \(y\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. In this expression, all terms contain the variable y, so their coefficients can be summed to simplify the expression.

Coefficients in Algebraic Expressions

A coefficient is the numerical factor in a term of an algebraic expression. Understanding how to add and subtract coefficients correctly is essential for simplifying expressions involving variables.

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing all possible operations. This process makes expressions easier to work with and understand, often by reducing the number of terms.

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Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. -p² - 7q + r

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Simplify each expression. See Example 8. 10 - (4y + 8)

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Find the given distances between points P, Q, R, and S on a number line, with coordinates -4, -1, 8, and 12, respectively. See Example 3. d (Q, R)

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