Problem 29 Multiply. $$\left(-4 x^{3} y^{... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 10: Problem 29

Multiply. $$\left(-4 x^{3} y^{4}\right)\left(2 x y^{2}\right)$$

Short Answer

Expert verified

ewline $-8x^{4}y^{6}$

Step by step solution

Identify the Expressions

We need to multiply the expressions $-4x^{3}y^{4}$ and $2xy^{2}$. First, identify the coefficients, variables, and their exponents in each expression.

Multiply the Coefficients

Multiply the numerical coefficients of the expressions: $-4 \text{ and } 2.$ \[-4 \times 2 = -8\]

Multiply the Variables

Multiply the variables by adding their exponents. For $x$-terms: \[x^{3} \times x = x^{3+1} = x^{4}.\] For $y$-terms: \[y^{4} \times y^{2} = y^{4+2} = y^{6}.\]

Combine Everything

Combine the results of the previous steps: \[-8x^{4}y^{6}.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coefficients

When multiplying monomials, the first step is to deal with the coefficients. Coefficients are the numerical parts of a term. In our problem, $-4x^{3}y^{4}$ and $2xy^{2}$, the coefficients are -4 and 2. To multiply the coefficients, simply perform the basic arithmetic operation: $-4 \times 2 = -8$. Once we have the product of the coefficients, we can move on to the variables.

Variables

Variables are the letters that represent unknown values in expressions. In our example, the variables are $x$ and $y$ found in both monomials: $-4x^{3}y^{4}$ and $2xy^{2}$. To multiply these variables, we need to take into account their exponents. Variables follow different rules than coefficients, particularly when it comes to combining them.

Exponents

Exponents indicate how many times a variable is multiplied by itself. In our given problem, we have $x^{3}$ and $x^{1}$ as well as $y^{4}$ and $y^{2}$. When multiplying variables with the same base, add their exponents.

Here is how it works for each variable:

For $x$-terms: $x^{3} \times x^{1} = x^{3+1} = x^{4}$
For $y$-terms: $y^{4} \times y^{2} = y^{4+2} = y^{6}$

By adding the exponents, we are combining the variables correctly for multiplication.

Multiplication of Variables

After understanding coefficients and exponents, the final step is to multiply variables together using the rule for exponents. We already determined that we add the exponents.

Now, let鈥檚 combine all the parts:

We multiply the coefficients: $-8$.
Combine $x$-terms: $x^{4}$.
Combine $y$-terms: $y^{6}$.

Therefore, the result of multiplying $-4x^{3}y^{4}$ and $2xy^{2}$ is $-8x^{4}y^{6}$. This detailed understanding should make it easier to grasp how to multiply monomials correctly.

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91影视

Multiply. $$\left(-4 x^{3} y^{4}\right)\left(2 x y^{2}\right)$$

Short Answer

Step by step solution

Identify the Expressions

Multiply the Coefficients

Multiply the Variables

Combine Everything

Key Concepts

Coefficients

Variables

Exponents

Multiplication of Variables

One App. One Place for Learning.

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