Answer :
To find the product of the given expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we need to follow these steps:
1. Break Down the Expression: We have three factors that need to be multiplied: [tex]\(7x^2\)[/tex], [tex]\(2x^3 + 5\)[/tex], and [tex]\(x^2 - 4x - 9\)[/tex].
2. Distribute One by One:
- First, distribute [tex]\(7x^2\)[/tex] across the terms in the second factor [tex]\((2x^3 + 5)\)[/tex].
[tex]\[
(7x^2)(2x^3) = 14x^5
\][/tex]
[tex]\[
(7x^2)(5) = 35x^2
\][/tex]
So after this step, we have:
[tex]\[
14x^5 + 35x^2
\][/tex]
3. Now Multiply with the Third Factor: Multiply this result by the third factor [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute [tex]\(14x^5\)[/tex] across [tex]\((x^2 - 4x - 9)\)[/tex].
[tex]\[
(14x^5)(x^2) = 14x^7
\][/tex]
[tex]\[
(14x^5)(-4x) = -56x^6
\][/tex]
[tex]\[
(14x^5)(-9) = -126x^5
\][/tex]
- Distribute [tex]\(35x^2\)[/tex] across [tex]\((x^2 - 4x - 9)\)[/tex].
[tex]\[
(35x^2)(x^2) = 35x^4
\][/tex]
[tex]\[
(35x^2)(-4x) = -140x^3
\][/tex]
[tex]\[
(35x^2)(-9) = -315x^2
\][/tex]
4. Combine All Terms: Now, combine all terms from each of these products to get a single expression.
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
5. Final Result: The expanded form of the expression is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is your expanded expression for the given product!
1. Break Down the Expression: We have three factors that need to be multiplied: [tex]\(7x^2\)[/tex], [tex]\(2x^3 + 5\)[/tex], and [tex]\(x^2 - 4x - 9\)[/tex].
2. Distribute One by One:
- First, distribute [tex]\(7x^2\)[/tex] across the terms in the second factor [tex]\((2x^3 + 5)\)[/tex].
[tex]\[
(7x^2)(2x^3) = 14x^5
\][/tex]
[tex]\[
(7x^2)(5) = 35x^2
\][/tex]
So after this step, we have:
[tex]\[
14x^5 + 35x^2
\][/tex]
3. Now Multiply with the Third Factor: Multiply this result by the third factor [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute [tex]\(14x^5\)[/tex] across [tex]\((x^2 - 4x - 9)\)[/tex].
[tex]\[
(14x^5)(x^2) = 14x^7
\][/tex]
[tex]\[
(14x^5)(-4x) = -56x^6
\][/tex]
[tex]\[
(14x^5)(-9) = -126x^5
\][/tex]
- Distribute [tex]\(35x^2\)[/tex] across [tex]\((x^2 - 4x - 9)\)[/tex].
[tex]\[
(35x^2)(x^2) = 35x^4
\][/tex]
[tex]\[
(35x^2)(-4x) = -140x^3
\][/tex]
[tex]\[
(35x^2)(-9) = -315x^2
\][/tex]
4. Combine All Terms: Now, combine all terms from each of these products to get a single expression.
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
5. Final Result: The expanded form of the expression is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is your expanded expression for the given product!
