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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 64
Chapter 1, Problem 64

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

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Recognize that the expression \( (3p + 5)^2 \) is a binomial squared, which means it can be expanded using the formula for the square of a binomial: \( (a + b)^2 = a^2 + 2ab + b^2 \).
Identify the terms in the binomial: here, \( a = 3p \) and \( b = 5 \).
Calculate the square of the first term: \( (3p)^2 = 9p^2 \).
Calculate twice the product of the two terms: \( 2 \times (3p) \times 5 = 30p \).
Calculate the square of the second term: \( 5^2 = 25 \). Then, combine all parts to write the expanded form: \( 9p^2 + 30p + 25 \).

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Key Concepts

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

Binomial Expansion

Binomial expansion involves expressing the power of a binomial, such as (a + b)^n, as a sum of terms using the Binomial Theorem or by applying algebraic identities. For the square of a binomial, (a + b)^2, the expansion is a^2 + 2ab + b^2.
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Algebraic Identities

Algebraic identities are formulas that simplify the process of expanding expressions. The identity (a + b)^2 = a^2 + 2ab + b^2 is essential for quickly expanding squared binomials without multiplying each term individually.
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Polynomial Operations

Polynomial operations include addition, multiplication, and simplification of polynomial expressions. Understanding how to multiply terms and combine like terms is crucial when expanding and simplifying expressions like (3p + 5)^2.
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