Distributive Law to Expand Expressions Including Binomials and Collect Like Terms (9)

Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (VCMNA306)

LO: To use the distributive law to expand expressions and collect like terms.
Know:

  • What the distributive law is
  • How to expand expressions using the distributive law
  • What are like terms
  • What are unlike terms
  • How to collect like terms to simplify expressions

Understand:

  • That the distributive law can be used to expand expressions and that like terms can be collected to simplify expressions.

Do:

  • I can use the distributive law to expand expressions and collect like terms.

Distributive Law

The distributive law means to multiply the coefficient (number/letters outside of the brackets) by all of the contents inside of the brackets.

In this case, the coefficient is k and I’m going to multiply it by “a” and “b”, which gives me a new expression of ka + kb.

In some cases, you have a binomial (an expression with 2 terms inside the brackets) multiplied by another binomial.

A quick strategy is to use the F.O.I.L method to expand the expressions.

F.O.I.L stands for first, outer, inner and last.

In this case, first you multiply the first of both brackets which is k x k, which gives you k^2.

Then you multiply both of the outer items of both brackets which is k x 3, which gives you 3k.

Then you multiply both of the inner items of both brackets which is 2 x k, which gives you 2k.

Finally, you multiply both of the last items of both brackets which is 2 x 3, which gives you 6.

When you put it all together you get k^2 + 3k + 2k + 6.

Since we know that 3k and 2k are like terms, we can simplify it by collecting like terms, which simplifies the expression to k^2 +5k +6.

Sometimes you’ll have binomials (an expression with 2 terms) with numbers and variables mixed.

Same quick strategy to use is the F.O.I.L method to expand the expressions.

F.O.I.L stands for first, outers, inners and last.

In this case, first you multiply the first of both brackets which is 4m x 3m, which gives you 12m^2.

Then you multiply both of the outer items of both brackets which is 4m x -5, which gives you -20m.

Then you multiply both of the inner items of both brackets which is 3m x -2, which gives you -6m.

Finally you multiply both of the last items of both brackets which is -2 x -5, which gives you +10 (two negatives make a positive).

When you put it all together you get 12m^2 -20m -6m + 10.

Since we know that -20m and -6m are like terms, we can simplify it by collecting like terms, which simplifies the expression to 12m^2-26m+10.

Binomial Distributive Law Videos

Textbook Questions

My Maths 9

Ex 2E pg. 79 Q. 3-5

My Maths 10

Ex 2C pg. 67 Q. 1-4