KS4. Algebra & Graphs. Expanding Brackets

Syllabus Objective: C2.2 Expand products of algebraic expressions (what does this mean)

Whenever we see something (i.e. a number or a letter) written in front of a bracket, it means that this something is multiplied by all of the terms inside the brackets.

• So, for instance 2(x-3) is equal to ?
• And -x(x-4) is equal to?

Also, if we have two expressions both in brackets, then all of the terms in the first expression must be multiplied by all of the terms in the second expression (N.B. if each expression has 2 terms, this means there will be four multiplications altogether)

• So, for instance (x+2)(x-3) is equal to ?
• And (x-7)(x-4) is equal to?

Practice with teacher

What if there is a letter outside of the brackets, like x(2x-3), or a term with a letter multiplied by something, like 4x(2x-3)?

Again, what would we do if there was a term with a letter multiplied by something (we call this a term with a coefficient of x), like (2x+3)(7x-8) or (9x-3)(8x-7).

Exercise

Now let’s complete exercise 11 on page 241 of the core textbook: