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Assignment - 3: Multiplying by a Monomial

Section [tex]$2 \propto 5$[/tex]

Question 2

Attempt 1 of 3

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is in place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Place the indicated product in the proper location on the grid.

[tex]\[
-4x^3y^2 \left(7xy^4\right)
\][/tex]

[tex]\[
\boxed{}
\][/tex]

1 2 3 4 5 6 17 18 9 13 14

[tex]\[
7^5 \quad 0^{\circ}
\][/tex]

[tex]\[
\boxed{} \boxed{} \boxed{a} \boxed{y} \boxed{} \boxed{} \boxed{}
\][/tex]



Answer :

GinnyAnswer
To solve the expression [tex]\(-4x^3y^2(7xy^4)\)[/tex], we need to multiply the coefficients, the [tex]\(x\)[/tex] terms, and the [tex]\(y\)[/tex] terms separately and then combine the results.

### Step-by-Step Solution:

1. Multiply the Coefficients:
- The coefficients we have are [tex]\(-4\)[/tex] and [tex]\(7\)[/tex].
- Multiplying these together: [tex]\(-4 \times 7 = -28\)[/tex].

2. Multiply the [tex]\(x\)[/tex] Terms:
- The [tex]\(x\)[/tex] terms in the expression are [tex]\(x^3\)[/tex] and [tex]\(x\)[/tex].
- To multiply these, add their exponents: [tex]\(3 + 1 = 4\)[/tex].
- So, [tex]\(x^3 \times x = x^4\)[/tex].

3. Multiply the [tex]\(y\)[/tex] Terms:
- The [tex]\(y\)[/tex] terms in the expression are [tex]\(y^2\)[/tex] and [tex]\(y^4\)[/tex].
- To multiply these, add their exponents: [tex]\(2 + 4 = 6\)[/tex].
- So, [tex]\(y^2 \times y^4 = y^6\)[/tex].

4. Combine the Results:
- The combined expression after multiplying everything is [tex]\(-28x^4y^6\)[/tex].

Therefore, the product of the expression [tex]\(-4x^3y^2(7xy^4)\)[/tex] is:

[tex]\[ -28x^4y^6 \][/tex]

This product should be placed in the answer box for the problem.

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