**Factorize completely 81a⁴ – 16b⁴**

**A.**** (3a + 2b)(2a – 3b)(9a ^{2} + 4b^{2})**

**B.**** (3a – 2b)(2a – 3b)(4a ^{2} – 9b^{2})**

**C.**** (3a – 2b)(3a + 2b)(9a ^{2} + 4b^{2})**

**D.**** (6a – 2b)(8a – 3b)(4a ^{3} – 9b^{2})**

**QUICK ANSWER…**

**C**

**DETAILS…**

**Factorizing ****completely ****the expression ****81a⁴ – 16b⁴**** will yield ****(3a – 2b)(3a + 2b)(9a ^{2} + 4b^{2})**

**.**

**Please note that:**

**Factorizing A****²****– B****² 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)(9a ^{2} + 4b^{2})**

**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, A****²****– B****² = (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 20****21**** JAMB-UTME**** MATHEMATICS**** question**** 35 ****/**