Answer :
To find the sum of the polynomials [tex]\( \left(7x^3 - 4x^2\right) \)[/tex] and [tex]\( \left(2x^3 - 4x^2\right) \)[/tex], follow these steps:
1. Align Like Terms:
- Both polynomials have terms that are "like terms," meaning they have the same variable raised to the same power. Here, we have [tex]\( x^3 \)[/tex] terms and [tex]\( x^2 \)[/tex] terms.
2. Add the Coefficients of Like Terms:
- For the [tex]\( x^3 \)[/tex] terms:
- The first polynomial has [tex]\( 7x^3 \)[/tex].
- The second polynomial has [tex]\( 2x^3 \)[/tex].
- Add these together: [tex]\( 7 + 2 = 9 \)[/tex].
- So, the result for the [tex]\( x^3 \)[/tex] term is [tex]\( 9x^3 \)[/tex].
- For the [tex]\( x^2 \)[/tex] terms:
- The first polynomial has [tex]\( -4x^2 \)[/tex].
- The second polynomial also has [tex]\( -4x^2 \)[/tex].
- Add these together: [tex]\( -4 + (-4) = -8 \)[/tex].
- So, the result for the [tex]\( x^2 \)[/tex] term is [tex]\( -8x^2 \)[/tex].
3. Combine the Results:
- The resulting polynomial after adding the polynomials is [tex]\( 9x^3 - 8x^2 \)[/tex].
Therefore, the sum of the polynomials [tex]\( \left(7x^3 - 4x^2\right) \)[/tex] and [tex]\( \left(2x^3 - 4x^2\right) \)[/tex] is [tex]\( 9x^3 - 8x^2 \)[/tex]. This matches option [tex]\( 9x^3 - 8x^2 \)[/tex] from the provided choices.
1. Align Like Terms:
- Both polynomials have terms that are "like terms," meaning they have the same variable raised to the same power. Here, we have [tex]\( x^3 \)[/tex] terms and [tex]\( x^2 \)[/tex] terms.
2. Add the Coefficients of Like Terms:
- For the [tex]\( x^3 \)[/tex] terms:
- The first polynomial has [tex]\( 7x^3 \)[/tex].
- The second polynomial has [tex]\( 2x^3 \)[/tex].
- Add these together: [tex]\( 7 + 2 = 9 \)[/tex].
- So, the result for the [tex]\( x^3 \)[/tex] term is [tex]\( 9x^3 \)[/tex].
- For the [tex]\( x^2 \)[/tex] terms:
- The first polynomial has [tex]\( -4x^2 \)[/tex].
- The second polynomial also has [tex]\( -4x^2 \)[/tex].
- Add these together: [tex]\( -4 + (-4) = -8 \)[/tex].
- So, the result for the [tex]\( x^2 \)[/tex] term is [tex]\( -8x^2 \)[/tex].
3. Combine the Results:
- The resulting polynomial after adding the polynomials is [tex]\( 9x^3 - 8x^2 \)[/tex].
Therefore, the sum of the polynomials [tex]\( \left(7x^3 - 4x^2\right) \)[/tex] and [tex]\( \left(2x^3 - 4x^2\right) \)[/tex] is [tex]\( 9x^3 - 8x^2 \)[/tex]. This matches option [tex]\( 9x^3 - 8x^2 \)[/tex] from the provided choices.
