Question

Perform the indicated operations. $$(3 x-2)^{2}$$

   Perform the indicated operations.
$$(3 x-2)^{2}$$

Algebra and Trigonometry

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 0, Problem 32

Instant Answer

Solved by Expert Ankit Gupta

07/04/2020

Step 1

We will apply the formula $(a-b)^{2} = a^{2} - 2ab + b^{2}$, where $a = 3x$ and $b = 2$. Show more…

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Perform the indicated operations. $$(3 x-2)^{2}$$

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Key Concepts

Distributive Property (FOIL Method)

The distributive property is a key concept in algebra that allows one to multiply each term in one expression by every term in another. In the context of squaring a binomial, it is often applied via the FOIL method (First, Outside, Inside, Last) to ensure that all pairwise products are accounted for, leading to the complete expansion of the expression.

Binomials

A binomial is an algebraic expression that contains exactly two terms, such as 3x and -2. Recognizing binomials is fundamental in algebra as they form the basis for more complex polynomial operations and manipulations.

Square of a Binomial

Squaring a binomial involves multiplying the binomial by itself. This process follows the formula (a - b)² = a² - 2ab + b² (or (a + b)² = a² + 2ab + b²), which simplifies the process by providing a direct expansion method. Understanding this formula is crucial for efficient polynomial expansion and simplification.

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