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Chapter 5: Problem 33

Find each product. $$5 x y^{2}\left(10 x^{2}-3 y\right)$$

Short Answer

Expert verified
The product is \(50 x^{3} y^{2} - 15 x y^{3}\).

Step by step solution

01

Identify the Terms

We can start by identifying the monomial and the binomial in the expression. The monomial is \(5xy^2\) and the binomial is \(10x^2 - 3y\).
02

Apply the distributive property

Muriply the monomial \(5x y^{2}\) with each term in the binomial \((10 x^{2}-3 y)\). Apply the rules of exponents and the operation multiplication on the identified terms. The multiplication results into: \(50 x^{3} y^{2} - 15 x y^{3}\).
03

Write the final answer

The final answer is \(50 x^{3} y^{2} - 15 x y^{3}\)

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Most popular questions from this chapter

Simplify: \(24+8 \cdot 3+28 \div(-7)\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$534.7=5.347 \times 10^{3}$$

Perform the indicated operations. $$(y+5)^{2}-(y-4)^{2}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I used the product rule for exponents to multiply \(x^{7}\) and \(y^{9}\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. It is not possible to write a binomial with degree \(0 .\)
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