Answer :
To find the sum of the given polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we will add the coefficients of the like terms separately.
Here are the steps:
1. Identify like terms: In both polynomials, we'll first identify the terms with the same variables raised to the same power. Here, we have terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex].
2. Add coefficients of the [tex]\(x^3\)[/tex] terms:
- The first polynomial has a term [tex]\(7x^3\)[/tex].
- The second polynomial has a term [tex]\(2x^3\)[/tex].
- Add these coefficients together: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined [tex]\(x^3\)[/tex] term is [tex]\(9x^3\)[/tex].
3. Add coefficients of the [tex]\(x^2\)[/tex] terms:
- The first polynomial has a term [tex]\(-4x^2\)[/tex].
- The second polynomial also has a term [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- Thus, the combined [tex]\(x^2\)[/tex] term is [tex]\(-8x^2\)[/tex].
4. Write the resulting polynomial:
- Combine the results from the steps above: [tex]\(9x^3 - 8x^2\)[/tex].
So, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Here are the steps:
1. Identify like terms: In both polynomials, we'll first identify the terms with the same variables raised to the same power. Here, we have terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex].
2. Add coefficients of the [tex]\(x^3\)[/tex] terms:
- The first polynomial has a term [tex]\(7x^3\)[/tex].
- The second polynomial has a term [tex]\(2x^3\)[/tex].
- Add these coefficients together: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined [tex]\(x^3\)[/tex] term is [tex]\(9x^3\)[/tex].
3. Add coefficients of the [tex]\(x^2\)[/tex] terms:
- The first polynomial has a term [tex]\(-4x^2\)[/tex].
- The second polynomial also has a term [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- Thus, the combined [tex]\(x^2\)[/tex] term is [tex]\(-8x^2\)[/tex].
4. Write the resulting polynomial:
- Combine the results from the steps above: [tex]\(9x^3 - 8x^2\)[/tex].
So, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
