Subtract: [tex]\left(6f^2 - 9f + 10\right) - \left(-2f^2 - f + 3\right)[/tex]

A. [tex]8f^2 - 8f + 7[/tex]
B. [tex]4f^2 - 10f + 7[/tex]
C. [tex]4f^2 - 10f + 13[/tex]
D. [tex]8f^2 - 10f + 7[/tex]



Answer :

To subtract the polynomials [tex]\( \left(6 f^2 - 9 f + 10\right) \)[/tex] and [tex]\( \left(-2 f^2 - f + 3\right) \)[/tex], we follow these steps:

1. Write down the polynomials:
[tex]\[ (6 f^2 - 9 f + 10) - (-2 f^2 - f + 3) \][/tex]

2. Distribute the negative sign across the second polynomial:
[tex]\[ 6 f^2 - 9 f + 10 + 2 f^2 + f - 3 \][/tex]

3. Combine like terms:

- For [tex]\( f^2 \)[/tex] terms:
[tex]\[ 6 f^2 + 2 f^2 = 8 f^2 \][/tex]

- For [tex]\( f \)[/tex] terms:
[tex]\[ -9 f + f = -8 f \][/tex]

- For constant terms:
[tex]\[ 10 - 3 = 7 \][/tex]

4. Put it all together:

[tex]\[ 8 f^2 - 8 f + 7 \][/tex]

So, the result of subtracting [tex]\( \left(6 f^2 - 9 f + 10\right) - \left(-2 f^2 - f + 3\right) \)[/tex] is:

[tex]\[ \boxed{8 f^2 - 8 f + 7} \][/tex]

Among the given choices, [tex]\( 8 f^2 - 8 f + 7 \)[/tex] is the correct answer.