Question

Select all expressions that are equivalent to 3q^4 −9q−10(−8q^2).

a. 3q^4+9q+80q^2
b. 3q^4−9q+80q^2
c. 3q^4 −9q−80q^2
d. 3q^4 +9q−80q^2

Answer 1

The equivalent expressions to 3q^4 -9q-10(-8q^2) are 3q^4+80q^2-9q and 3q^4-9q+80q^2, which correspond to Option b as the order of the terms in a polynomial does not impact its equivalence.

Step-by-step explanation:

The student is asked to identify which expressions are equivalent to 3q^4 −9q−10(−8q^2). Multiplying −10 by −8q^2 gives +80q^2, so the original expression simplifies to 3q^4 −9q + 80q^2. Therefore, the equivalent expressions are:

• 3q^4+80q^2−9q (Option b)
• 3q^4−9q+80q^2 (Also Option b since the order of the terms doesn't alter the expression)

Options a, c, and d are not equivalent because they either have incorrect signs or the terms are ordered differently, which does not necessarily mean the expressions are different.