Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], follow these steps:
1. Identify like terms:
- Both polynomials have terms with [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
- In the expression [tex]\((7x^3 - 4x^2)\)[/tex], the terms are [tex]\(7x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
- In the expression [tex]\((2x^3 - 4x^2)\)[/tex], the terms are [tex]\(2x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of similar terms:
- For the [tex]\(x^3\)[/tex] terms: Add [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex]:
[tex]\[
7 + 2 = 9
\][/tex]
So, the combined term for [tex]\(x^3\)[/tex] is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: Add [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex]:
[tex]\[
-4 + (-4) = -8
\][/tex]
So, the combined term for [tex]\(x^2\)[/tex] is [tex]\(-8x^2\)[/tex].
3. Write the expression for the sum:
- Combine the results of the like terms. The sum of the polynomials is:
[tex]\[
9x^3 - 8x^2
\][/tex]
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify like terms:
- Both polynomials have terms with [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
- In the expression [tex]\((7x^3 - 4x^2)\)[/tex], the terms are [tex]\(7x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
- In the expression [tex]\((2x^3 - 4x^2)\)[/tex], the terms are [tex]\(2x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of similar terms:
- For the [tex]\(x^3\)[/tex] terms: Add [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex]:
[tex]\[
7 + 2 = 9
\][/tex]
So, the combined term for [tex]\(x^3\)[/tex] is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: Add [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex]:
[tex]\[
-4 + (-4) = -8
\][/tex]
So, the combined term for [tex]\(x^2\)[/tex] is [tex]\(-8x^2\)[/tex].
3. Write the expression for the sum:
- Combine the results of the like terms. The sum of the polynomials is:
[tex]\[
9x^3 - 8x^2
\][/tex]
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
