Factorize completely 81a⁴ – 16b⁴
A. (3a + 2b)(2a – 3b)(9a2 + 4b2)
B. (3a – 2b)(2a – 3b)(4a2 – 9b2)
C. (3a – 2b)(3a + 2b)(9a2 + 4b2)
D. (6a – 2b)(8a – 3b)(4a3 – 9b2)
QUICK ANSWER…
C
DETAILS…
Factorizing completely the expression 81a⁴ – 16b⁴ will yield (3a – 2b)(3a + 2b)(9a2 + 4b2).
Please note that:
- Factorizing A² – B² will give (A + B)(A – B).
Thus,
81a⁴ – 16b⁴ = 9²a⁴ – 4²b⁴
= (9a²)² – (4b²)², applying our rule stated above, we have:
= (9a² + 4b²)(9a² – 4b²)
At this stage you should be able to suspect options A and C. let's solve further to find out…
= (9a² + 4b²)(9a² – 4b²)
= (9a² + 4b²)(3²a² – 2²b²)
= (9a² + 4b²)((3a)² – (2b)²)
= (9a² + 4b²)(3a + 2b)( 3a – 2b)
Rearranging, we have:
(3a – 2b)(3a + 2b)(9a2 + 4b2)
Now for the right answer to the above question:
- Option A is incorrect.
- Option B is not correct.
- C is correct.
- D is not the correct answer.
KEY-POINTS…
You may please note these/this:
- In factorization, A² – B² = (A + B)(A – B).
- You can use this simple rule to quickly dissolve so many similar problems.
If you love our answers, you can simply join our community and also provide answers like this, fellow learners like you will appreciate it.
/ culled from 2021 JAMB-UTME MATHEMATICS question 35 /
