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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. R - Algebra ReviewProblem 45
Chapter 1, Problem 45

Find each product. See Example 5. (4r - 1) (7r + 2)

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1
Identify the two binomials to be multiplied: \((4r - 1)\) and \((7r + 2)\).
Apply the distributive property (also known as the FOIL method) to multiply each term in the first binomial by each term in the second binomial: First, Outer, Inner, Last.
Multiply the First terms: \(4r \times 7r = 28r^{2}\).
Multiply the Outer terms: \(4r \times 2 = 8r\).
Multiply the Inner terms: \(-1 \times 7r = -7r\), and multiply the Last terms: \(-1 \times 2 = -2\). Then combine like terms \$8r\( and \)-7r$ to simplify the expression.

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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 each term inside one parenthesis by each term inside the other. For example, in (a + b)(c + d), you multiply a by c and d, then b by c and d, combining all products.
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Imaginary Roots with the Square Root Property

Multiplying Binomials

Multiplying binomials involves applying the distributive property twice, often remembered as FOIL (First, Outer, Inner, Last). This method ensures all terms are multiplied correctly to form a polynomial.
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Multiplying Complex Numbers

Combining Like Terms

After multiplying, you combine like terms—terms with the same variable and exponent—to simplify the expression into its simplest polynomial form.
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Adding and Subtracting Complex Numbers
Related Practice
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Multiply or divide, as indicated. See Example 3. ((m² + 3m + 2) / (m² + 5m + 4)) ÷ ((m² + 5m + 6) / (m² + 10m + 24))

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Textbook Question

Find each product. See Example 5. (3x + 1) (2x - 7)

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Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(0)

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Find each product or quotient where possible. See Example 2. -0.06(0.4)

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Find each product or quotient where possible. See Example 2. -24 -4

Textbook Question

Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. g(-2)