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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], you need to add the coefficients of the like terms together.
Let's break it down step-by-step:
1. Identify like terms:
- Both polynomials have [tex]\(x^3\)[/tex] terms and [tex]\(x^2\)[/tex] terms.
2. Add the coefficients of [tex]\(x^3\)[/tex]:
- In the first polynomial [tex]\((7x^3 - 4x^2)\)[/tex], the coefficient of [tex]\(x^3\)[/tex] is 7.
- In the second polynomial [tex]\((2x^3 - 4x^2)\)[/tex], the coefficient of [tex]\(x^3\)[/tex] is 2.
- Adding these coefficients together: [tex]\(7 + 2 = 9\)[/tex].
3. Add the coefficients of [tex]\(x^2\)[/tex]:
- In the first polynomial, the coefficient of [tex]\(x^2\)[/tex] is -4.
- In the second polynomial, the coefficient of [tex]\(x^2\)[/tex] is also -4.
- Adding these coefficients together: [tex]\(-4 + (-4) = -8\)[/tex].
4. Combine the results:
- The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
So, the polynomial resulting from the sum is [tex]\(9x^3 - 8x^2\)[/tex].
The correct answer is: [tex]\(9x^3 - 8x^2\)[/tex].
Let's break it down step-by-step:
1. Identify like terms:
- Both polynomials have [tex]\(x^3\)[/tex] terms and [tex]\(x^2\)[/tex] terms.
2. Add the coefficients of [tex]\(x^3\)[/tex]:
- In the first polynomial [tex]\((7x^3 - 4x^2)\)[/tex], the coefficient of [tex]\(x^3\)[/tex] is 7.
- In the second polynomial [tex]\((2x^3 - 4x^2)\)[/tex], the coefficient of [tex]\(x^3\)[/tex] is 2.
- Adding these coefficients together: [tex]\(7 + 2 = 9\)[/tex].
3. Add the coefficients of [tex]\(x^2\)[/tex]:
- In the first polynomial, the coefficient of [tex]\(x^2\)[/tex] is -4.
- In the second polynomial, the coefficient of [tex]\(x^2\)[/tex] is also -4.
- Adding these coefficients together: [tex]\(-4 + (-4) = -8\)[/tex].
4. Combine the results:
- The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
So, the polynomial resulting from the sum is [tex]\(9x^3 - 8x^2\)[/tex].
The correct answer is: [tex]\(9x^3 - 8x^2\)[/tex].
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