Answer :
To find the product of [tex]\((7x^2)(2x^3+5)(x^2-4x-9)\)[/tex], we'll follow these steps:
1. Distribute and expand the expression step by step.
2. Start by multiplying the first two expressions:
[tex]\[
(7x^2)(2x^3 + 5) = 7x^2 \times 2x^3 + 7x^2 \times 5
\][/tex]
[tex]\[
= 14x^5 + 35x^2
\][/tex]
3. Now multiply the result by the third expression [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2)(x^2 - 4x - 9)
\][/tex]
Distribute each term:
- Multiply [tex]\(14x^5\)[/tex] by each term:
[tex]\[
14x^5 \times x^2 = 14x^7
\][/tex]
[tex]\[
14x^5 \times (-4x) = -56x^6
\][/tex]
[tex]\[
14x^5 \times (-9) = -126x^5
\][/tex]
- Multiply [tex]\(35x^2\)[/tex] by each term:
[tex]\[
35x^2 \times x^2 = 35x^4
\][/tex]
[tex]\[
35x^2 \times (-4x) = -140x^3
\][/tex]
[tex]\[
35x^2 \times (-9) = -315x^2
\][/tex]
4. Combine like terms to form the final expression:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
So the expanded and final form of the product is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
1. Distribute and expand the expression step by step.
2. Start by multiplying the first two expressions:
[tex]\[
(7x^2)(2x^3 + 5) = 7x^2 \times 2x^3 + 7x^2 \times 5
\][/tex]
[tex]\[
= 14x^5 + 35x^2
\][/tex]
3. Now multiply the result by the third expression [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2)(x^2 - 4x - 9)
\][/tex]
Distribute each term:
- Multiply [tex]\(14x^5\)[/tex] by each term:
[tex]\[
14x^5 \times x^2 = 14x^7
\][/tex]
[tex]\[
14x^5 \times (-4x) = -56x^6
\][/tex]
[tex]\[
14x^5 \times (-9) = -126x^5
\][/tex]
- Multiply [tex]\(35x^2\)[/tex] by each term:
[tex]\[
35x^2 \times x^2 = 35x^4
\][/tex]
[tex]\[
35x^2 \times (-4x) = -140x^3
\][/tex]
[tex]\[
35x^2 \times (-9) = -315x^2
\][/tex]
4. Combine like terms to form the final expression:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
So the expanded and final form of the product is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
