Question Video: Factoring an Expression with a Common Binomial Term Mathematics • Second Year of Preparatory School

Video Transcript

Fully factor the expression 𝑥 multiplied by 𝑥 plus three plus two multiplied by 𝑥 plus three.

Upon inspection, we observe that the two parts of this expression share a common binomial factor of 𝑥 plus three. We can, therefore, factor by this shared binomial. In the first part of the expression, this binomial is multiplied by 𝑥. And in the second part, it is multiplied by two. Hence, overall, it is multiplied by 𝑥 plus two. And so, 𝑥 multiplied by 𝑥 plus three plus two multiplied by 𝑥 plus three is equal to 𝑥 plus two multiplied by 𝑥 plus three. This expression cannot be factored any further as the two terms in each binomial do not share any common factors other than one.