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Answer :
Let's find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex].
1. Identify like terms:
- Both polynomials have [tex]\(x^3\)[/tex] terms, [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- Both polynomials have [tex]\(x^2\)[/tex] terms, [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of like terms:
- For the [tex]\(x^3\)[/tex] terms: Add the coefficients 7 and 2.
[tex]\[
7 + 2 = 9
\][/tex]
So, the term for [tex]\(x^3\)[/tex] in the summed polynomial is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: Add the coefficients [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex].
[tex]\[
-4 + (-4) = -8
\][/tex]
So, the term for [tex]\(x^2\)[/tex] in the summed polynomial is [tex]\(-8x^2\)[/tex].
3. Write the result as a single polynomial:
- Combine the terms:
[tex]\[
9x^3 - 8x^2
\][/tex]
Thus, 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 [tex]\(x^3\)[/tex] terms, [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- Both polynomials have [tex]\(x^2\)[/tex] terms, [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of like terms:
- For the [tex]\(x^3\)[/tex] terms: Add the coefficients 7 and 2.
[tex]\[
7 + 2 = 9
\][/tex]
So, the term for [tex]\(x^3\)[/tex] in the summed polynomial is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: Add the coefficients [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex].
[tex]\[
-4 + (-4) = -8
\][/tex]
So, the term for [tex]\(x^2\)[/tex] in the summed polynomial is [tex]\(-8x^2\)[/tex].
3. Write the result as a single polynomial:
- Combine the terms:
[tex]\[
9x^3 - 8x^2
\][/tex]
Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
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