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Chapter 5: Problem 48

Find each product of the monomial and the polynomial. $$4 y^{2}\left(5 y^{2}-6 y+3\right)$$

Short Answer

Expert verified
The product of the monomial and the polynomial is \(20y^4 - 24y^3 + 12y^2\).

Step by step solution

01

Applying the distributive Property

Multiply each term in the polynomial \((5y^2 - 6y + 3)\) by the monomial \(4y^2\). In other words, apply the distributive property which states that \(a(b + c + d) = ab + ac + ad\). So, we get: \[4y^2*5y^2 + 4y^2*(-6y) + 4y^2*3\]
02

Carry out the multiplication

Carry out the multiplication as indicated in each of the terms in step 1. In the multiplication of two powers with the same base, we add the exponents as per the laws of exponents. This gives us: \[20y^4 - 24y^3 + 12y^2\]

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Most popular questions from this chapter

Explain how to simplify an expression that involves a quotient raised to a power. Provide an example with your explanation.

Use a vertical format to find each product. $$\begin{array}{r}9 y^{3}-7 y^{2}+5 y \\\3 y^{2}+5 y \\\\\hline\end{array}$$

Perform the indicated operations. $$(x+5)(x-6)-(x+2)(x-9)$$

How do you know if an exponential expression is simplified?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)
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