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Chapter 0: Problem 43

In Exercises 15鈥�58, find each product. $$ (2 x+3)^{2} $$

Short Answer

Expert verified
The product of \((2x + 3)^2\) is \(4x^2 + 12x + 9\).

Step by step solution

01

Identify a and b

In this problem, the expression \((2x+3)^2\) is the square of the binomial \(2x+3\). So, \(a = 2x\) and \(b = 3\).
02

Apply the formula for a perfect square

Substitute \(a = 2x\) and \(b = 3\) into the formula \(a^2 + 2ab + b^2\). This gives \((2x)^2 + 2*(2x)*(3) + (3)^2\).
03

Simplify

Calculate \(a^2\), \(2ab\), and \(b^2\) to get \(4x^2 + 12x + 9\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Perfect Square Trinomials
Understanding perfect square trinomials is essential when working with binomial products. A perfect square trinomial is the result of squaring a binomial. It takes the form of \(a^2 + 2ab + b^2\), where \(a\) and \(b\) are any numbers, variables, or expressions.

Consider the exercise \((2x+3)^2\). Here, we have the binomial \(2x+3\) being squared, which results in a perfect square trinomial after expansion. Performing the calculations, we start by squaring each term (\

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Most popular questions from this chapter

Factor Completely. $$(y+1)^{3}+1$$

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