Question

select all of the expressions equivalent to 21a - 7a^3. select all that apply. a. 7a(3 - a^2) b. -7a(3 + a^2) c. 7(3a - a^3) d. 7(3a^2 - a^2) e. -7a(-3 + a^2)

Explanation:

Step1: Factor the given expression

Factor out the greatest - common factor from \(21a - 7a^{3}\). The GCF of \(21a\) and \(7a^{3}\) is \(7a\). So, \(21a - 7a^{3}=7a(3 - a^{2})\). Also, \(7a(3 - a^{2})=7(3a - a^{3})\) and \(7a(3 - a^{2})=-7a(- 3 + a^{2})\).

Step2: Analyze each option

• Option A: \(7a(3 - a^{2})\), which is equivalent to \(21a - 7a^{3}\) after factoring out the GCF.
• Option B: \(-7a(3 + a^{2})=-21a-7a^{3}\), not equivalent.
• Option C: \(7(3a - a^{3}) = 21a - 7a^{3}\), equivalent.
• Option D: \(7(3a^{2}-a^{2})=7\times2a^{2}=14a^{2}\), not equivalent.
• Option E: \(-7a(-3 + a^{2})=21a - 7a^{3}\), equivalent.

Answer:

A. \(7a(3 - a^{2})\), C. \(7(3a - a^{3})\), E. \(-7a(-3 + a^{2})\)