Dear learners

In this lesson we're looking at determining the product of a binomial and a trinomial. In grade 8 & 9 you learnt what a binomial is and what a trinomial is. 

Binomial - an algebraic expression consisting of 2 terms

Trinomial - an algebraic expression consisting of 3 terms.

The product of a binomial and a trinomial can be determined by applying the distributive law.

This is where we multiply an outside term with each and every term that's inside the brackets.

Examples :

1. (2x – 3y) (2x²- 3xy + 7y²)

= 2x (2x²- 3xy + 7y²) – 3y (2x²- 3xy + 7y²)

= 4x³ – 6x²y + 14xy² – 6x²y + 9xy² – 21y³

= 4x³ – 12x²y + 23xy² – 21y³

2. (x -1) (x² – x + 1)

= x(x² – x + 1) – 1(x² – x + 1)

= x³ – x² + x – x² + x - 1

= x³ – 2x² + 2x -1

Please answer the following questions at the back of your mathematics exercise book, you don't have to submit it as it will be marked in the next lesson.

1. Find the product of the following:

a) (a – 1) (2a² + a + 1)

b) (2a + 3) (4a² – 6a + 9)

c) (3x² + xy – 2y²) (x + 2y)