What you need to know

Things to remember:

  • To expand a single bracket, we multiply what is inside a bracket by what is outside the bracket.
  • When multiplying by a negative number it changes the sign.
    • A negative multiplied by a negative is positive.
    • A positive multiplied by a negative is negative.

Expand and simplify 4(3x-4)

Before we can do this, we need to answer 3 questions:

  • What is multiplication?
  • What does 4(3x-4) mean?
  • What does “expand” mean?
  • What does “simplify” mean?

So, what is multiplication? Multiplication is a quick way of writing lots of additions.

4\times3=3+3+3+3=12

4\times x=x+x+x+x=4x

What does 4(3x-4) mean? Well, something is missing. Let’s start by thinking about what 4x means. Well, if we look at the last equation we did, we can see that it means “4 multiplied by x”, there was an invisible \times symbol. Well, there is an invisible \times symbol between the 4 and (3x-4) as well.

4(3x-4)=4\times(3x-4)

What does “expand” mean? Well, this just means to do the multiplication!

Hint: Remember, multiplication just means adding the same things multiple times.

 

4(3x-4)=4\times(3x-4)=(3x-4)+(3x-4)+(3x-4)+(3x-4)

 

Finally, what does “simplify” mean? This just means that we want it in its simplest form, which we do by collecting like terms!

(3x-4)+(3x-4)+(3x-4)+(3x-4)=3x+3x+3x+3x-4-4-4-4

3x+3x+3x+3x-4-4-4-4 =12x-16

4(3x-4)= 12x-16

Notice how the final answer is actually just what is inside bracket multiplied by what is outside!

4\times3x= 12x

4\times-4= -16

So, we can actually expand and simplify a bracket by just multiplying what is inside the bracket by what is outside it.

3(8x+2)=3\times8x+ 3\times2=24x+6

7(11x-5)=7\times11x-7\times5=77x-35

a(b+c)=a\times b+ a\times c=ab+ac

Example Questions

12(2-3x)=12\times2-12\times3x=24-36x

a(3b-2a)=a\times3b-a\times2a=3ab-2a^2

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