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Answer :
To find the sum of the given polynomials, we need to add them together by combining like terms. Let's go through the steps:
1. Identify the polynomials:
The two polynomials given are:
- Polynomial 1: [tex]\(7x^3 - 4x^2\)[/tex]
- Polynomial 2: [tex]\(2x^3 - 4x^2\)[/tex]
2. Add the coefficients of like terms:
- For the [tex]\(x^3\)[/tex] terms:
- The coefficient from Polynomial 1 is 7.
- The coefficient from Polynomial 2 is 2.
- Adding these coefficients gives [tex]\(7 + 2 = 9\)[/tex].
- So, the term for [tex]\(x^3\)[/tex] in the sum is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms:
- The coefficient from Polynomial 1 is -4.
- The coefficient from Polynomial 2 is -4.
- Adding these coefficients gives [tex]\(-4 + (-4) = -8\)[/tex].
- So, the term for [tex]\(x^2\)[/tex] in the sum is [tex]\(-8x^2\)[/tex].
3. Write the resulting polynomial:
Combine the terms we found from adding like terms:
[tex]\[
9x^3 - 8x^2
\][/tex]
So, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
1. Identify the polynomials:
The two polynomials given are:
- Polynomial 1: [tex]\(7x^3 - 4x^2\)[/tex]
- Polynomial 2: [tex]\(2x^3 - 4x^2\)[/tex]
2. Add the coefficients of like terms:
- For the [tex]\(x^3\)[/tex] terms:
- The coefficient from Polynomial 1 is 7.
- The coefficient from Polynomial 2 is 2.
- Adding these coefficients gives [tex]\(7 + 2 = 9\)[/tex].
- So, the term for [tex]\(x^3\)[/tex] in the sum is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms:
- The coefficient from Polynomial 1 is -4.
- The coefficient from Polynomial 2 is -4.
- Adding these coefficients gives [tex]\(-4 + (-4) = -8\)[/tex].
- So, the term for [tex]\(x^2\)[/tex] in the sum is [tex]\(-8x^2\)[/tex].
3. Write the resulting polynomial:
Combine the terms we found from adding like terms:
[tex]\[
9x^3 - 8x^2
\][/tex]
So, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
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