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 55
Chapter 1, Problem 55

Find each product. See Example 5. (5r - 3t²)²

Verified step by step guidance
1
Recognize that the expression is a square of a binomial: \((5r - 3t^{2})^{2}\). This means you will use the formula for the square of a binomial: \((a - b)^{2} = a^{2} - 2ab + b^{2}\).
Identify the terms \(a\) and \(b\) in the binomial: here, \(a = 5r\) and \(b = 3t^{2}\).
Calculate the square of the first term: \(a^{2} = (5r)^{2} = 25r^{2}\).
Calculate twice the product of the two terms: \(-2ab = -2 \times 5r \times 3t^{2} = -30rt^{2}\).
Calculate the square of the second term: \(b^{2} = (3t^{2})^{2} = 9t^{4}\). Then, combine all parts to write the expanded expression as \(25r^{2} - 30rt^{2} + 9t^{4}\).

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.

Binomial Expansion

Binomial expansion involves expanding expressions raised to a power, such as (a + b)². It follows the formula (a + b)² = a² + 2ab + b², which helps in simplifying and finding the product of binomials.
Recommended video:
3:42
Rationalizing Denominators Using Conjugates

Polynomial Multiplication

Polynomial multiplication requires multiplying each term in one polynomial by every term in the other. This process ensures all products are accounted for and combined correctly to simplify the expression.
Recommended video:
5:35
Introduction to Quadratic Equations

Exponents and Like Terms

Understanding exponents is crucial when squaring terms, as powers multiply (e.g., (t²)² = t⁴). Combining like terms after expansion simplifies the expression by adding coefficients of terms with the same variables and exponents.
Recommended video:
4:28
Introduction to Inverse Trig Functions
Related Practice
Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. 1 ƒ(x) = x + —— x⁵

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6.

center (0, 4), radius 4

1
views
Textbook Question

Evaluate each expression. See Example 5. -|5|

4
views
Textbook Question

Add or subtract, as indicated. See Example 4. ((17y + 3)/(9y + 7)) - ((-10y - 18)/(9y + 7 ))

6
views
Textbook Question

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27

3
views
Textbook Question

Evaluate each expression. See Example 5. |3⁄2|