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Chapter 5: Problem 43

Find each product. $$(3 x y-1)(5 x y+2)$$

Short Answer

Expert verified
The product of the two binomials is \(15x^2y^2 + xy - 2\)

Step by step solution

01

Apply the distributive property

First, distribute the terms in the first parenthesis by the terms in the second using the distributive property. The distributive property states that \(a(b + c) = ab + ac\). Similarly, we can also distribute a subtraction, which we will need for the -1 in the first parenthesis. Thus, the multiplication of the two binomials will become: \(3xy(5xy) + 3xy(2) -1(5xy) - 1(2)\)
02

Simplify the multiplication

The next step is to simplify the multiplication inside each term. We do this by multiplying the coefficients and the variables separately: \(15x^2y^2 + 6xy - 5xy - 2\)
03

Combine like terms

Finally we combine like terms to simplify the expression. Like terms are terms that contain the same variables raised to the same power. In this case \(6xy\) and \(-5xy\) are like terms and can be combined to \(xy\): \(15x^2y^2 + xy - 2\)

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Most popular questions from this chapter

Find the missing coefficients and exponents designated by question marks. $$\frac{3 x^{14}-6 x^{12}-7 x^{7}}{2 x^{7}}=-x^{7}+2 x^{5}+3$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(2 y+7)^{2}=4 y^{2}+28 y+49$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Each statement applies to the division problem $$\frac{x^{3}+1}{x+1}$$ There's no need to apply the long-division process to this problem because I can work the problem in my head and see that the quotient must be \(x^{2}+1\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I divide monomials by dividing coefficients and subtracting exponents.

Express \(\frac{7}{8}\) as a decimal.
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