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Chapter 0: Problem 65

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

Short Answer

Expert verified
The product is \(49x^2 + 70xy + 25y^2\).

Step by step solution

01

Identify the Terms

The given binomial is \((7 x + 5 y)^{2}\). Here, \(a = 7x\) and \(b = 5y\).
02

Apply the Binomial Expansion Formula

According to the formula: \((a + b)^2 = a^2 + 2ab + b^2\), we substitute \(a\) and \(b\) with \(7x\) and \(5y\) respectively to get the expanded binomial.
03

Calculate each Term

Square each term: \((7x)^2 = 49x^2\), \(2*(7x)*(5y) = 70xy\), and \((5y)^2 = 25y^2\).
04

Put It All Together

Combine all the calculated terms: \(49x^2 + 70xy + 25y^2 \). This is the product of the given binomial square.

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