Factorise fully year 8 maths

[veryworried1988]

A bit stuck as the answers have been marked wrong but without the correct answers. (Can't do the indices so typed squared)

1. 24xsquared + 18x
   I got 2x(12x+9)

2. 45xysquared + 54xsquaredysquared
   I got 9xy(5y + 6xy)

If you expand, it gets back to the question, I thought that was the test to check if you have factorised correctly.

What have me and dd done wrong?

Thanks

Top one needs 6 outside the bracket.

Second one needs y- squared outside the bracket.

So you factorised, but didn't factorise fully.

6x(4x+3)

9xy-squared(5+6x)

thank you @TeenToTwenties

how would I know that, is there a strategy? For the first 1, because 6 is outside the brackets, it would be 4 and 3 in the brackets, how is that correct when 2 x 12 is 24 and 2 x 9 is 18?

Because inside the brackets you still left things with common factors. 18 is 2x9 but it is also 6x3.

You left 12x+9 but 12 and 9 are both divisible by 3 so you need to take the 3 outside the bracket too. That us the 'fully' bit of the request.

Similarly in second question both your terms in the bracket had a y so that needed to go outside the bracket too.

For indices, the convention is to do a caret, followed by the index number.

So x squared is represented by x^2. Mumsnet formatting interferes with this though!

You want the highest common factor, because the objective is to get the coefficient inside the brackets (the number before the x^2) as low as possible

So 24x^2 +18x

then
6(4x^2+3x).

This is to make it easier to calculate the value of x later.

@AstonUniversityPotholeDepartment unfortunately MN formatting turns ^ into italics ....

(X-post with the edit!)

Yes, I've just discovered that the very hard way. I fixed it with line breaks, but I should have foreseen it in the first place!

I see!!!! the penny has dropped, thank you. I shall practise with more examples so i can help dd.

Super.

You may get onto fractions, whereby you fully factorise top and bottom, then simplify by dividing top and bottom by any factors they share.

Eg (4xy +24y) / ( 6y-8xy)
Goes to
4y(x+6)/2y(3-4x)
Then
2(x+6)/(3-4x)

Wouldn't factorise fully mean that no elements could be further factorised?

24X² + 18X
is
6(4X² + 3X)
is
2 × 3 × X (4X + 3)

The factors are
2
3
X
and
(4X + 3)
(Apologies if the multiplication signs × look too similar to the letter X. Equals signs seem to mean "superbold" too!)

@CrabSignalArmy I would say no, not normally when doing algebra. If they wanted that they would usually mention prime factors.

Happy to be corrected by someone such as @noblegiraffe though.

Factorise fully just means that the highest common factor of the terms is outside the brackets.
So in the first example 2x(12x+9) is factorised. You would have also factorised it if you wrote x(24x+18).
but 6x(4x+3) is fully factorised as you have taken out all common factors.

It's similar to writing a fraction in its simplest form, you can't simplify it any further.