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Answer :
To find the sum of the given polynomials, we combine like terms from each polynomial individually:
1. Identify like terms:
- The terms with [tex]\( x^3 \)[/tex] are [tex]\( 7x^3 \)[/tex] and [tex]\( 2x^3 \)[/tex].
- The terms with [tex]\( x^2 \)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the like terms:
- For the [tex]\( x^3 \)[/tex] terms: Add [tex]\( 7 \)[/tex] and [tex]\( 2 \)[/tex]. This gives [tex]\( 9x^3 \)[/tex].
- For the [tex]\( x^2 \)[/tex] terms: Add [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex]. This results in [tex]\(-8x^2\)[/tex].
3. Combine the results:
- The sum of the polynomials is therefore [tex]\( 9x^3 - 8x^2 \)[/tex].
So, the correct option for the sum of the polynomials [tex]\(\left(7x^3 - 4x^2\right) + \left(2x^3 - 4x^2\right)\)[/tex] is [tex]\( 9x^3 - 8x^2 \)[/tex].
1. Identify like terms:
- The terms with [tex]\( x^3 \)[/tex] are [tex]\( 7x^3 \)[/tex] and [tex]\( 2x^3 \)[/tex].
- The terms with [tex]\( x^2 \)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the like terms:
- For the [tex]\( x^3 \)[/tex] terms: Add [tex]\( 7 \)[/tex] and [tex]\( 2 \)[/tex]. This gives [tex]\( 9x^3 \)[/tex].
- For the [tex]\( x^2 \)[/tex] terms: Add [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex]. This results in [tex]\(-8x^2\)[/tex].
3. Combine the results:
- The sum of the polynomials is therefore [tex]\( 9x^3 - 8x^2 \)[/tex].
So, the correct option for the sum of the polynomials [tex]\(\left(7x^3 - 4x^2\right) + \left(2x^3 - 4x^2\right)\)[/tex] is [tex]\( 9x^3 - 8x^2 \)[/tex].
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