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Factorize completely 81a⁴ – 16b⁴

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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:

  1. Option A is incorrect.
  2. Option B is not correct.
  3. C is correct.
  4. 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.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 35 /

1 Answers

  1. 0 Votes Thumb up 0 Votes Thumb down 0 Votes

    In factorization, A² – B² = (A + B)(A – B), please note this, very important.

    Admin - Mar 30, 2022 | Reply


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