Question Video: Factoring a Monomial Completely

Video Transcript

Completely factor the following expression: 39 𝑥 squared 𝑦 squared.

To factor this expression, we need to write it as a product of numbers and algebraic terms that can’t be simplified any further. We’ll begin by writing the number 39 as the product of its prime factors. 39 is equal to 13 multiplied by three. Both 13 and three are prime numbers. So 39 can’t be broken down any further. As a product of prime factors, 39 is equal to 13 multiplied by three.

So 39𝑥 squared 𝑦 squared can be written as 13 multiplied by three multiplied by 𝑥 squared multiplied by 𝑦 squared. We can factor this expression further. 𝑥 squared can be written as 𝑥 multiplied by 𝑥 and 𝑦 squared can be written as 𝑦 multiplied by 𝑦.

Therefore, the completely factorized form of the expression 39𝑥 squared 𝑦 squared is 13 multiplied by three multiplied by 𝑥 multiplied by 𝑥 multiplied by 𝑦 multiplied by 𝑦.