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Chapter 5: Problem 39

Find each product. $$(x+5 y)(7 x+3 y)$$

Short Answer

Expert verified
The product of given expressions is \(7x^2 + 38xy + 15y^2\).

Step by step solution

01

Apply the Distributive Law to First Term

Start by multiplying the first term in the first parentheses \(x\) with each term in the second parentheses. This gives \(x \cdot 7x + x \cdot 3y\), which simplifies to \(7x^2 + 3xy\).
02

Apply the Distributive Law to Second Term

Next, multiply the second term in the first parentheses \(5y\) with each term in the second parentheses. This gives \(5y \cdot 7x + 5y \cdot 3y\), which simplifies to \(35xy + 15y^2\).
03

Combine Like Terms

Combine the expressions obtained from Step 1 and Step 2 together: \(7x^2 + 3xy + 35xy + 15y^2\). This can be further simplified by combining like terms which results in \(7x^2 + 38xy + 15y^2\).

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Most popular questions from this chapter

Explain how to divide monomials. Give an example.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. When a certain polynomial is divided by \(2 x+4,\) the quotient is $$x-3+\frac{17}{2 x+4}$$ What is the polynomial?

Solve the system: $$\left\\{\begin{array}{l}7 x-6 y=17 \\\3 x+y=18\end{array}\right.$$ (Section 4.3, Example 2)

$$\text { Graph: } y=\frac{1}{3} x$$

Will help you prepare for the material covered in the next section. $$\text { Simplify: } \frac{\left(x^{2}\right)^{3}}{5^{3}}$$
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