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Chapter 5: Problem 46

Find each product. $$(2 x+5 y)^{2}$$

Short Answer

Expert verified
The product of the given binomial expression is \(4x^2 + 20xy + 25y^2\).

Step by step solution

01

Identify the elements

In this problem, \(a\) is represented by the term \(2x\) while \(b\) is represented by the term \(5y\).
02

Use the binomial square formula

Apply the binomial square formula \((a + b)^2 = a^2 + 2ab + b^2 \). Substitute \(a\) with \(2x\) and \(b\) with \(5y\).
03

Compute each term

Calculate the square of \(a\) which is \((2x)^2 = 4x^2\), the product of \(2ab\) which is \(2 * 2x * 5y = 20xy\), and the square of \(b\) which is \((5y)^2 = 25y^2\).
04

Form the final equation

Combine all the computed terms to form the final equation. This gives \(a^2 + 2ab + b^2 = 4x^2 + 20xy + 25y^2 \).

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