Skip to main content
Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 65
Chapter 1, Problem 65

Perform the indicated operations. −3(4q2−3q+2)+2(−q2+q−4)-3(4q^2-3q+2) + 2(-q^2+q-4)

Verified step by step guidance
1
Identify the expression to simplify: \(-3(4q^2 - 3q + 2) + 2(-q^2 + q - 4)\).
Distribute the constants outside the parentheses to each term inside the parentheses: multiply \(-3\) by each term in \((4q^2 - 3q + 2)\) and multiply \(2\) by each term in \((-q^2 + q - 4)\).
Write the distributed terms explicitly: \(-3 \times 4q^2\), \(-3 \times (-3q)\), \(-3 \times 2\), and \(2 \times (-q^2)\), \(2 \times q\), \(2 \times (-4)\).
Simplify each multiplication to get the new terms: \(-12q^2\), \(+9q\), \(-6\), \(-2q^2\), \(+2q\), and \(-8\).
Combine like terms by grouping the \(q^2\) terms together, the \(q\) terms together, and the constant terms together to write the simplified expression.

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 allows you to multiply a single term by each term inside a parenthesis. For example, a(b + c) = ab + ac. This property is essential for expanding expressions like -3(4q^2 - 3q + 2) by multiplying -3 with each term inside the parentheses.
Recommended video:
Guided course
04:15
Multiply Polynomials Using the Distributive Property

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For instance, 4q^2 and -2q^2 are like terms and can be combined to 2q^2. This step simplifies the expression after distribution.
Recommended video:
5:22
Combinations

Polynomial Operations

Polynomial operations include addition, subtraction, and multiplication of polynomial expressions. Understanding how to perform these operations correctly is crucial for simplifying expressions such as the given problem, which involves multiplying and then adding polynomials.
Recommended video:
Guided course
8:38
Performing Row Operations on Matrices
Related Practice
Textbook Question

Perform the indicated operations. (3p+5)2

11
views
Textbook Question

Factor each polynomial. See Examples 5 and 6. (a+b)2-16

1
views
Textbook Question

Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∛√4

1
views
Textbook Question

Add or subtract as indicated. Write answers in lowest terms as needed. 7/9 - 2/9

Textbook Question

Factor each polynomial. See Examples 5 and 6. 36z2−81y436z^2-81y^4

Textbook Question

Insert ⊆ or ⊈ in each blank to make the resulting statement true. {1, 5} ____ {0, 1, 2, 3, 5}