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 37
Chapter 1, Problem 37

Find each product. (m-n+k)(m+2n-3k)

Verified step by step guidance
1
Identify the two binomials to be multiplied: \((m - n + k)\) and \((m + 2n - 3k)\).
Apply the distributive property (also known as the FOIL method for binomials) by multiplying each term in the first polynomial by each term in the second polynomial.
Multiply each term step-by-step: - \(m \times m\), - \(m \times 2n\), - \(m \times (-3k)\), - \((-n) \times m\), - \((-n) \times 2n\), - \((-n) \times (-3k)\), - \(k \times m\), - \(k \times 2n\), - \(k \times (-3k)\).
Write down all the products obtained from the previous step as a sum: \(m^2 + 2mn - 3mk - nm - 2n^2 + 3nk + km + 2kn - 3k^2\).
Combine like terms by grouping terms with the same variables and powers to simplify the expression.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

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

Polynomial Multiplication

Polynomial multiplication involves multiplying each term in one polynomial by every term in the other polynomial. This process requires applying the distributive property to combine like terms and simplify the expression.
Recommended video:
03:42
Finding Zeros & Their Multiplicity

Distributive Property

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis, which is essential when expanding products of polynomials.
Recommended video:
Guided course
04:15
Multiply Polynomials Using the Distributive Property

Combining Like Terms

After multiplying polynomials, terms with the same variables and exponents must be combined to simplify the expression. This step ensures the final product is written in its simplest form.
Recommended video:
5:22
Combinations
Related Practice
Textbook Question

Find each product. (3w+2)(-w2+4w-3)

3
views
Textbook Question

Find each sum or difference. 4 - 9

1
views
Textbook Question

Find each root. ∛x³

Textbook Question

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. (-4)-3

Textbook Question

Insert ∈ or ∉ in each blank to make the resulting statement true. . 0 ____ ∅

Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. 223⋅1352\(\frac{2}{3}\) \(\cdot\) 1\(\frac{3}{5}\)

4
views
1
rank