Question

factor 6a^2-54

Answer 1

first - what is the common factor between 6 and 54?

Answer 2

2?

Answer 3

what is 6 * 9 ?

Answer 4

54

Answer 5

so the common factor must be 6.
so we can pul this out and re-write the equation as:

6(a^2-9)

Answer 6

next - do you know the following factorisation:\[a^2-b^2=(a+b)(a-b)\]

Answer 7

would it be (x+6)(x-6)??

Answer 8

no

Answer 9

then what is it?? lol

Answer 10

are you aware that \(a^2-b^2\) can be factorised as \((a+b)(a-b)\)?

Answer 11

it's known as the difference between two squares

Answer 12

im confused.

Answer 13

have you been taught about the factorisation involving the difference between two squares?

i.e. have you been taught that:\[a^2-b^2=(a+b)(a-b)\]

Answer 14

no

Answer 15

ok, if we expand this expression: \((a+b)(a-b)\) you will se that we get:\[(a+b)(a-b)=a(a-b)+b(a-b)=a^2-ab+ab-b^2=a^2-b^2\]so this shows that if you have an expression involving the difference of two squares \(a^2\) and \(b^2\) then you can always factorise it as \((a+b)(a-b)\)

Answer 16

now what we ended up with in your question was:\[6(a^2-9)\]so should notice that 9 can be written as \(3^2\), so we can re-write this as:\[6(a^2-3^2)\]now notice we have a difference of two squares within the braces