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Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], you need to follow these steps:
1. Identify Like Terms: Look for terms in each polynomial that have the same degree. In this case, the like terms are the terms involving [tex]\(x^3\)[/tex] and the terms involving [tex]\(x^2\)[/tex].
2. Combine Like Terms for [tex]\(x^3\)[/tex]:
- From the first polynomial, [tex]\((7x^3 - 4x^2)\)[/tex], the term is [tex]\(7x^3\)[/tex].
- From the second polynomial, [tex]\((2x^3 - 4x^2)\)[/tex], the term is [tex]\(2x^3\)[/tex].
- Add these terms together: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Combine Like Terms for [tex]\(x^2\)[/tex]:
- From the first polynomial, the term for [tex]\(x^2\)[/tex] is [tex]\(-4x^2\)[/tex].
- From the second polynomial, the term for [tex]\(x^2\)[/tex] is also [tex]\(-4x^2\)[/tex].
- Add these terms together: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
4. Write the Resulting Polynomial: After combining the like terms, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
1. Identify Like Terms: Look for terms in each polynomial that have the same degree. In this case, the like terms are the terms involving [tex]\(x^3\)[/tex] and the terms involving [tex]\(x^2\)[/tex].
2. Combine Like Terms for [tex]\(x^3\)[/tex]:
- From the first polynomial, [tex]\((7x^3 - 4x^2)\)[/tex], the term is [tex]\(7x^3\)[/tex].
- From the second polynomial, [tex]\((2x^3 - 4x^2)\)[/tex], the term is [tex]\(2x^3\)[/tex].
- Add these terms together: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Combine Like Terms for [tex]\(x^2\)[/tex]:
- From the first polynomial, the term for [tex]\(x^2\)[/tex] is [tex]\(-4x^2\)[/tex].
- From the second polynomial, the term for [tex]\(x^2\)[/tex] is also [tex]\(-4x^2\)[/tex].
- Add these terms together: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
4. Write the Resulting Polynomial: After combining the like terms, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
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