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Chapter 0: Problem 73

Find each product. $$(7 x+5 y)^{2}$$

Short Answer

Expert verified
The product of \((7 x+5 y)^{2}\) is \(49x^2 + 70xy + 25y^2\).

Step by step solution

01

Understanding the Problem

We are given a square of a binomial. The term \((7 x+5 y)^{2}\) should be understood as \((7x+5y)*(7x+5y)\). Hence, we have to multiply the binomial by itself.
02

Expanding the Binomial

We will use the formula \((a+b)^2 = a^2+2ab+b^2\), where \(a\) is \(7x\) and \(b\) is \(5y\). Substituting these terms in place of \(a\) and \(b\), we have \((7x)^2+2*(7x)*(5y)+(5y)^2\).
03

Simplifying the Expression

Simplify each term in the expanded expression: \(49x^2 + 70xy + 25y^2\).

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