Question

Find the difference.

(6a^2 − 7− 3a^3) − (7 + a^3 + 2a^2)

(A) −4a^3 + 8a^2 + 14
(B) −2a^3 − 4a^2 − 14
(C) −4a^3 + 4a^2
(D)−4a^3 + 4a^2 − 14

Answer 1

4a^2 - 4a^3 - 14

Explanation:

Step 1: First, we can distribute the negative to each term in the second expression:

6a^2 - 7 - 3a^3 -7 - a^3 - 2a^2

Step 2: Now we can simplify by combining like terms:

(6a^2 - 2a^2) + (-3a^3 - a^3) + (-7 - 7)

4a^2 - 4a^3 - 14

Thus, the difference of (6a^2 − 7− 3a^3) − (7 + a^3 + 2a^2) is 4a^2 - 4a^3 - 14

Optional Step 3: We can check that we've found the correct difference by plugging in a number for the variable a in both the expression we used to find the difference, (6a^2 − 7− 3a^3) − (7 + a^3 + 2a^2), and the expression we think is the difference, 4a^2 - 4a^3 - 14.

If we get the same value for both when we plug in a, we've correctly found the difference:

Plugging in 2 for a in (6a^2 − 7− 3a^3) − (7 + a^3 + 2a^2):

(6(2)^2 - 7 - 3(2)^3) - (7 + 2^3 + 2(2)^2)

(6 * 4 - 7 - 3 * 8) - (7 + 8 + 2 * 4)

(24 - 7 - 24) - (15 + 8)

(17 - 24) -23

-7 - 23

-30

Plugging in 2 for a in 4a^2 - 4a^3 - 14:

4(2)^2 - 4(2)^3 - 14

4 * 4 - 4 * 8 - 14

16 - 32 - 14

-16 - 14

-30

Thus, we've correctly found the difference of the two expressions

Answer 2

D.
Combine like terms.