Answer :
Let's find the product of the expressions [tex]\((3a^2 \cdot 4ax + x^2)\)[/tex] and [tex]\((5x^3 - 2ay)\)[/tex].
1. Simplify the First Expression:
The first expression is [tex]\(3a^2 \cdot 4ax + x^2\)[/tex].
- Simplify [tex]\(3a^2 \cdot 4ax\)[/tex]:
[tex]\[
3a^2 \times 4a \times x = 12a^3x
\][/tex]
- The first expression becomes:
[tex]\[
12a^3x + x^2
\][/tex]
2. Write down the Second Expression:
The second expression is [tex]\(5x^3 - 2ay\)[/tex].
3. Distribute and Multiply:
To find the product, distribute each term in the first expression through the second expression.
- Multiply [tex]\(12a^3x\)[/tex] by each term in the second expression:
- [tex]\(12a^3x \times 5x^3 = 60a^3x^4\)[/tex]
- [tex]\(12a^3x \times (-2ay) = -24a^4xy\)[/tex]
- Multiply [tex]\(x^2\)[/tex] by each term in the second expression:
- [tex]\(x^2 \times 5x^3 = 5x^5\)[/tex]
- [tex]\(x^2 \times (-2ay) = -2ax^2y\)[/tex]
4. Combine all the results:
Collect all the products obtained from distributing and simplify:
[tex]\[
-24a^4xy + 60a^3x^4 - 2ax^2y + 5x^5
\][/tex]
Thus, the product of the given expressions is:
[tex]\[
-24a^4xy + 60a^3x^4 - 2ax^2y + 5x^5
\][/tex]
This doesn't exactly match any given option, as the answers either contain errors or were formatted in a non-standard way. Always ensure the solution process is followed closely for accuracy.
1. Simplify the First Expression:
The first expression is [tex]\(3a^2 \cdot 4ax + x^2\)[/tex].
- Simplify [tex]\(3a^2 \cdot 4ax\)[/tex]:
[tex]\[
3a^2 \times 4a \times x = 12a^3x
\][/tex]
- The first expression becomes:
[tex]\[
12a^3x + x^2
\][/tex]
2. Write down the Second Expression:
The second expression is [tex]\(5x^3 - 2ay\)[/tex].
3. Distribute and Multiply:
To find the product, distribute each term in the first expression through the second expression.
- Multiply [tex]\(12a^3x\)[/tex] by each term in the second expression:
- [tex]\(12a^3x \times 5x^3 = 60a^3x^4\)[/tex]
- [tex]\(12a^3x \times (-2ay) = -24a^4xy\)[/tex]
- Multiply [tex]\(x^2\)[/tex] by each term in the second expression:
- [tex]\(x^2 \times 5x^3 = 5x^5\)[/tex]
- [tex]\(x^2 \times (-2ay) = -2ax^2y\)[/tex]
4. Combine all the results:
Collect all the products obtained from distributing and simplify:
[tex]\[
-24a^4xy + 60a^3x^4 - 2ax^2y + 5x^5
\][/tex]
Thus, the product of the given expressions is:
[tex]\[
-24a^4xy + 60a^3x^4 - 2ax^2y + 5x^5
\][/tex]
This doesn't exactly match any given option, as the answers either contain errors or were formatted in a non-standard way. Always ensure the solution process is followed closely for accuracy.
