Question

When subtracting 3x2 + 4x + 9 from 15x2 + 6x − 12, which TWO choices are correct? A) Write the problem as 3x2 + 4x + 9 − (15x2 + 6x − 12). B) Write the problem as 15x2 + 6x − 12 − (3x2 + 4x + 9). C) The difference is −12x2 − 2x + 3. D) The difference is 12x2 + 10x − 3. E) The difference is 12x2 + 2x − 21.

Answer 1

B + E

Explanation:

Simplify the following:

-(3 x^2 + 4 x + 9) + 15 x^2 + 6 x - 12

Hint: | Distribute -1 over 3 x^2 + 4 x + 9.

-(3 x^2 + 4 x + 9) = -3 x^2 - 4 x - 9:

-3 x^2 - 4 x - 9 + 15 x^2 + 6 x - 12

Hint: | Group like terms in 15 x^2 - 3 x^2 + 6 x - 4 x - 12 - 9.

Grouping like terms, 15 x^2 - 3 x^2 + 6 x - 4 x - 12 - 9 = (15 x^2 - 3 x^2) + (6 x - 4 x) + (-12 - 9):

(15 x^2 - 3 x^2) + (6 x - 4 x) + (-12 - 9)

Hint: | Combine like terms in 15 x^2 - 3 x^2.

15 x^2 - 3 x^2 = 12 x^2:

12 x^2 + (6 x - 4 x) + (-12 - 9)

Hint: | Combine like terms in 6 x - 4 x.

6 x - 4 x = 2 x:

12 x^2 + 2 x + (-12 - 9)

Hint: | Evaluate -12 - 9.

-12 - 9 = -21:

Answer: 12 x^2 + 2 x + -21