Year 12s: what will be the first way you research your future options? >>

stuck on a question help -maths

Herah

2xsquared-11xy+5ysquared

FACTORISE

Reply 1

Groggy Moggy

2x^2 -11xy +5y^2 take your time reading this so you fully understand it! (I hope :wink:

)

First try taking a logical approach. You know that to get that x^2 (x squared) you need an x in each bracket; because we have 2x^2 we need 2x in one bracket and x in the other (2x +- ?y)(x +- ?y). Hopefully you are with me so far. Then we must look and see what our values for a, b and c are... You are familiar with the quadratic equation?

a=2 b=-11 and c=5 in this case...

When solving normal quadratic equations where 'coefficient' a (that number in front of x^2) is more than 1, we can use the technique of multiplying c and a to get a value. so 2 times 5 is 10 here. What are the factors of 10 that add to make -11? That would be -1 and -10 (they multiply to make 10 and add to make -11). Now for the important part...

If we then rewrite out the equation as 2x^2 -1xy /// -10xy +5y^2 we can factorise each half like so: x (2x-y) and then -5y (2x-y). We then combine the two parts outside the brackets ( I have underlined them to make it obvious) to make a new bracket and multiply this with the other bracket (that remains the same for each 'half' factorisation above): (x-5y) (2x-y)

Okay; if we multiply out these two brackets we get our original equation. Whew that was a heavy explanation- it assumes a fair bit of prior knowledge (i.e. that you know how to factorise a normal quadratic with one unknown). Hope this helps! :smile:

Ask ur teacher if you are still unsure, or you can go here where it is explained in general http://www.onlinemathlearning.com/factor-trinomials-two-variables.html

Reply 2

Hunarench95

Original post by Herah

2xsquared-11xy+5ysquared

FACTORISE

(2x-y)(x-5y) :smile:

Posted from TSR Mobile

Reply 3

Hunarench95

It's gets easier the more you practice. Just spend an hour doing a set of factorising questions and it should come a little easier

Posted from TSR Mobile

Reply 4

brianeverit

Original post by Herah

2xsquared-11xy+5ysquared

FACTORISE

In general, to factorise

Px^2+Qxy+Ry^2

we can proceed as follows.
Let

(ax+by)(cx+dy)=acx^2+(ad+bc)xy+bdy^2=Px^2+Qxy+Ry^2

List every possible pair of values of a and c that make ac=P, Similarly list possible values of b and d that make bd=R.
Take each pair of (a,c) with each pair of (b,d) and calculate ad and bc . If R>0 then b and d must have the same sign, i.e they must either both be positive or both negative. If they are both positive then we want ad+bc=Q, but if they are both negative we want either ad-bc=Q or bc-ad=Q. It sounds a long drawn out process but you should soon get used to it and do it quite quickly. You only have to try different pairs of values of (ac) and (bd) until you find one that fits., and often there is only one pair to try anyway, as in the example you have given where 2x^2 can only be x and 2x and 5y^2 can only be y and 5y and if no pair works t5hen the quadratic will not factorise..