How can you know when to either simplify with powers, by factorising or with quadratics?

I think I understand the methods but I just get confused when given a question whether to use the simplifying with powers or simplifying by factorising method

Please help! A quick answer would be much appreciated....

### 1 Answer | Add Yours

When you to siplify an expression then

(i) see powers of the same variable in terms .

(ii) We know we can not add or subtract powers ,so way out for this factor out like powers.

(iii) factoring is not possible then only think about spiliting the middle terms in case quadratic expression or completing the square and write epression as product of two /three factors.

`3x^2+14x-5`

in this expression we three terms.

all have different power ,so factoring not possible.

next try to split middle term 14x

5 x 3=15 ,sign of 5 is (-)

factor 15 in two parts such as their difference is 14

15=15 x 1

`3x^2+(15-1)x-5`

`3x^2+15x-x-5`

`3x(x+5)-1(x+5)`

`(x+5)(3x-1)`

this simple method.

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