Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], follow these steps:
1. Combine the like terms:
First, identify the like terms in each polynomial.
- The terms involving [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms involving [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the like terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. Hence, the [tex]\(x^3\)[/tex] term in the sum is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. Hence, the [tex]\(x^2\)[/tex] term in the sum is [tex]\(-8x^2\)[/tex].
3. Write the resulting polynomial:
Combine the results from step 2 to form the sum of the polynomials:
[tex]\[
9x^3 - 8x^2
\][/tex]
4. Select the correct answer from the options provided:
From the options given:
- [tex]\(5x^3\)[/tex]
- [tex]\(9x^3\)[/tex]
- [tex]\(5x^3 - 8x^2\)[/tex]
- [tex]\(9x^3 - 8x^2\)[/tex]
We see that [tex]\(9x^3 - 8x^2\)[/tex] matches the result we obtained.
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is:
[tex]\[
\boxed{9x^3 - 8x^2}
\][/tex]
1. Combine the like terms:
First, identify the like terms in each polynomial.
- The terms involving [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms involving [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the like terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. Hence, the [tex]\(x^3\)[/tex] term in the sum is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. Hence, the [tex]\(x^2\)[/tex] term in the sum is [tex]\(-8x^2\)[/tex].
3. Write the resulting polynomial:
Combine the results from step 2 to form the sum of the polynomials:
[tex]\[
9x^3 - 8x^2
\][/tex]
4. Select the correct answer from the options provided:
From the options given:
- [tex]\(5x^3\)[/tex]
- [tex]\(9x^3\)[/tex]
- [tex]\(5x^3 - 8x^2\)[/tex]
- [tex]\(9x^3 - 8x^2\)[/tex]
We see that [tex]\(9x^3 - 8x^2\)[/tex] matches the result we obtained.
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is:
[tex]\[
\boxed{9x^3 - 8x^2}
\][/tex]
