Skip to main content
Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. R - Algebra ReviewProblem R.2.123
Chapter 1, Problem R.2.123

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 5k + 3k

Verified step by step guidance
1
Identify the common factor in the expression \(5k + 3k\). Here, both terms have the variable \(k\).
Use the distributive property, which states that \(a b + a c = a (b + c)\), to factor out the common variable \(k\) from both terms.
Rewrite the expression as \(k (5 + 3)\) by factoring out \(k\).
Simplify the expression inside the parentheses by adding the numbers: \(5 + 3\).
Write the simplified expression as \(k \times 8\) or simply \$8k$.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

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

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend individually by the number and then adding the results. In algebraic terms, a(b + c) = ab + ac. This property helps simplify expressions by factoring or expanding terms.
Recommended video:
2:20
Imaginary Roots with the Square Root Property

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, 5k and 3k are like terms because both contain the variable k. Adding their coefficients simplifies the expression to 8k.
Recommended video:
3:18
Adding and Subtracting Complex Numbers

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing operations such as addition, subtraction, multiplication, or division. Simplifying 5k + 3k involves using the distributive property and combining like terms to get a more concise expression.
Recommended video:
6:36
Simplifying Trig Expressions
Related Practice
Textbook Question

Evaluate each expression. See Example 4. (-2)⁴

4
views
Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. (-(p + 2)² - 3r)/(2 - q)

Textbook Question

Simplify each expression. See Example 8. -6p + 5 - 4p + 6 + 11p

Textbook Question

Evaluate each expression. See Example 5. 5 - 7 • 3 - (-2)³

5
views
Textbook Question

Evaluate each expression. See Example 4. -2⁴

Textbook Question

Evaluate each expression. See Example 5. -8 + (-4) (-6) ÷ 12 4 - (-3)