Problem 73 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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 \((7x)^2+2*(7x)*(5y)+(5y)^2\).

Step 3: Simplifying the Expression

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