Maths: Basic simplification help

I'm doing C1 Maths and I got this question:

Expand and simplify if possible:
9(x - 2)

Easy, right? I got:
9x - 18

However, why can't I simplify this even more? So by dividing '9x' and '-18' by 9? So I would get:
x - 2

Why isn't this correct?

Thank you

Reply 1

the bear

20

9x - 18 is not equivalent to x - 2

if you put in a value for x you get two different results....

Reply 2

JPencil

9

Expansion is right but 9x-18 is not equivalent to x-2. You can only divided by a factor when you have an equation, you have an expression :wink:

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Reply 3

username1646063

17

Original post by Edwarric

I'm doing C1 Maths and I got this question:

Expand and simplify if possible:
9(x - 2)

Easy, right? I got:
9x - 18

However, why can't I simplify this even more? So by dividing '9x' and '-18' by 9? So I would get:
x - 2

Why isn't this correct?

Thank you

Basically u expanded the brackets correctly however,u can't simplify it further as X needs a value.

Eg. . 9x - 18
If u replace X as a number two =18
So 18- 18=0

I duno if this is right tho

Reply 4

Doctor_Einstein

19

Original post by Edwarric

I'm doing C1 Maths and I got this question:

Expand and simplify if possible:
9(x - 2)

Easy, right? I got:
9x - 18

However, why can't I simplify this even more? So by dividing '9x' and '-18' by 9? So I would get:
x - 2

Why isn't this correct?

Thank you

9x - 18 has a common factor of 9, so taking this out gives,

9(x - 2), not (x-2) as your post suggests.

Reply 5

the bear

20

simplifying means you change your original expression into a new ( simpler ) one but which is still equivalent to the original one.
to test for equivalence put a value into both expressions instead of x... the two results must be the same ...

Reply 6

Callum Scott

2

I'll try to teach you something here :tongue:

There are equations and then there are expressions.

Expressions

An expression has no equals symbols and no solutions can be determined because there is nothing to determine a solution for.

Example:

2x+3

This is an expression, there are no solutions because there's nothing that it is equal to, it is simply a statement.

When dealing with expressions, they can be simplified, but not solved.
The simplified form of an expression must be equivalent to the original, or else it isn't the same expression. This means, no adding/subtracting/multiplying/dividing etc. , only factoring. We use the

\equiv

symbol to signify that it is equivalent. This is only used for equating expressions.

Example:

(x+2)(x+4) \equiv x^2 + 6x + 8

_{If you tried to solve this expression, any value of x would 'satisfy' it, because the expressions are defined to be equal in the first place. It is not an equation.}

_{$2(3x+6) \equiv 6(x+2)$}
_{Dividing both sides of the expression by 2}_changes_{the expression; yes, they'd be equivalent, but the 2 new expressions would differ from the original, so there'd be no point!}

Equations

Equations utilise the equals sign we all know and love,

=

. They can be solved and/or they can be simplified.

If we want to find the

x

axis intercepts for the graph

y = x^2 - 6x + 8

, what we're in fact doing is looking for a solution such that

x^2 - 6x + 8 = 0

, or

y = 0

.

If we have the equation:

2y = 2x^2 -12x +16

,

We can simplify the equation because both sides have an unnecessary factor of 2. If you think about

2y=2x

, any input value of

x

would still be equal to the output value,

y

, regardless of whether the 2s were there or not.

It can be said¹that:

(2y = 2x^2 -12x + 16) \equiv (y = x^2 -6x + 8) \equiv (y = (x-4)(x-2))

If you have any more questions, or if someone finds a problem with what I've written, please ask/tell me :h:

Maths: Basic simplification help

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