Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex], we need to combine the like terms.
1. Combine the [tex]\(x^3\)[/tex] terms:
- Start with the coefficients of [tex]\(x^3\)[/tex] in both polynomials. The first polynomial has a coefficient of [tex]\(7\)[/tex] and the second has a coefficient of [tex]\(2\)[/tex].
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined term for [tex]\(x^3\)[/tex] is [tex]\(9x^3\)[/tex].
2. Combine the [tex]\(x^2\)[/tex] terms:
- Now look at the coefficients of [tex]\(x^2\)[/tex]. The first polynomial has a coefficient of [tex]\(-4\)[/tex] and the second also has [tex]\(-4\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- Thus, the combined term for [tex]\(x^2\)[/tex] is [tex]\(-8x^2\)[/tex].
Finally, write the resulting polynomial by combining these terms:
[tex]\[ 9x^3 - 8x^2 \][/tex]
So, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
1. Combine the [tex]\(x^3\)[/tex] terms:
- Start with the coefficients of [tex]\(x^3\)[/tex] in both polynomials. The first polynomial has a coefficient of [tex]\(7\)[/tex] and the second has a coefficient of [tex]\(2\)[/tex].
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined term for [tex]\(x^3\)[/tex] is [tex]\(9x^3\)[/tex].
2. Combine the [tex]\(x^2\)[/tex] terms:
- Now look at the coefficients of [tex]\(x^2\)[/tex]. The first polynomial has a coefficient of [tex]\(-4\)[/tex] and the second also has [tex]\(-4\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- Thus, the combined term for [tex]\(x^2\)[/tex] is [tex]\(-8x^2\)[/tex].
Finally, write the resulting polynomial by combining these terms:
[tex]\[ 9x^3 - 8x^2 \][/tex]
So, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
