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Chapter 5: Problem 45

Find each product. $$(2 x+3 y)^{2}$$

Short Answer

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

Step by step solution

01

Identify the elements of the binomial

The binomial contains two elements: \(a = 2x\) and \(b = 3y\). The binomial is squared, and in order to simplify it, the formula for the square of a binomial \((a + b)^2 = a^2 + 2ab + b^2\) must be used.
02

Apply the formula

By applying the formula for squaring a binomial, compute the square of a, 2ab, and the square of b and add them together. This could be completed as follows: \((2x)^2 + 2(2x)(3y) + (3y)^2\), simplifying to \(4x^2 + 12xy + 9y^2\).
03

Finalize the solution

The final result of the square of the binomial \((2x + 3y)^2\) is \(4x^2 + 12xy + 9y^2\).

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