Answer :
To find the product of the given expressions [tex]\(\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)\)[/tex], let's break down the steps:
1. Multiply the first two expressions:
- Start with [tex]\((7x^2)(2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] over each term in the second expression:
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- So, the result of multiplying the first two expressions is [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
- Now, we need to multiply [tex]\((14x^5 + 35x^2)\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute [tex]\(14x^5\)[/tex] across each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [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]
- Distribute [tex]\(35x^2\)[/tex] across each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [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]
3. Add all the terms together:
- Combine all the terms from the expansion:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
Thus, the product of [tex]\(\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)\)[/tex] is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
1. Multiply the first two expressions:
- Start with [tex]\((7x^2)(2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] over each term in the second expression:
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- So, the result of multiplying the first two expressions is [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
- Now, we need to multiply [tex]\((14x^5 + 35x^2)\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute [tex]\(14x^5\)[/tex] across each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [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]
- Distribute [tex]\(35x^2\)[/tex] across each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [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]
3. Add all the terms together:
- Combine all the terms from the expansion:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
Thus, the product of [tex]\(\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)\)[/tex] is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
