Question

Lily was given the following problem:
−
(
3
b
2
c
3
)
2
Which of the following choices demonstrate an accurate way to simplify this expression?
Select ALL that apply.
Select all that apply
A
−
(
3
b
2
c
3
)
(
3
b
2
c
3
)
=
−
9
b
4
c
6

B
(
−
3
)
b
2
+
2
c
3
+
2
=
−
3
b
4
c
5

C
(
−
3
)
b
2
⋅
2
c
3
⋅
2
=
−
3
b
4
c
6

D
−
(
3
2
b
2
⋅
2
c
3
⋅
2
)
=
−
9
b
4
c
6

Answer 1

Correct choices: A and D.

Why:
- A: (−(3b^2c^3))^2 = −(3b^2c^3)(3b^2c^3) = −9b^4c^6 — valid.
- D: using exponent rules, (3b^2c^3)^2 = 3^2(b^2)^2(c^3)^2 = 9 b^{4} c^{6}, then the leading minus gives −9b^4c^6 — also valid.

B and C are incorrect:
- B misuses + and gives wrong exponents/terms.
- C incorrectly expands the square as multiplying by factors 2 and produces the wrong coefficient and exponents.