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Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex], we need to add the coefficients of the like terms.
1. Add the coefficients of the [tex]\(x^3\)[/tex] terms:
- The coefficient of [tex]\(x^3\)[/tex] in the first polynomial is 7.
- The coefficient of [tex]\(x^3\)[/tex] in the second polynomial is 2.
- Adding these coefficients: [tex]\(7 + 2 = 9\)[/tex].
2. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
- The coefficient of [tex]\(x^2\)[/tex] in the first polynomial is [tex]\(-4\)[/tex].
- The coefficient of [tex]\(x^2\)[/tex] in the second polynomial is [tex]\(-4\)[/tex].
- Adding these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
3. Form the resulting polynomial:
- The resulting polynomial, after combining terms, is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
1. Add the coefficients of the [tex]\(x^3\)[/tex] terms:
- The coefficient of [tex]\(x^3\)[/tex] in the first polynomial is 7.
- The coefficient of [tex]\(x^3\)[/tex] in the second polynomial is 2.
- Adding these coefficients: [tex]\(7 + 2 = 9\)[/tex].
2. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
- The coefficient of [tex]\(x^2\)[/tex] in the first polynomial is [tex]\(-4\)[/tex].
- The coefficient of [tex]\(x^2\)[/tex] in the second polynomial is [tex]\(-4\)[/tex].
- Adding these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
3. Form the resulting polynomial:
- The resulting polynomial, after combining terms, is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
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