Algebraic manipulation involves rearranging variables to make an algebraic expression better suit your needs. During this rearrangement, the value of the expression does not change.
Algebraic expressions aren't always given in their most convenient forms. This is where algebraic manipulation comes in.
What value of satisfies
We can rearrange this equation for by putting the terms with on one side and the constant terms on the other.
Algebraic manipulation is also used to simplify complicated-looking expressions by factoring and using identities. Let's walk through an example:
If and , find the value of
It's possible to solve for and and plug those values into this expression, but the algebra would be very messy. Instead, we can rearrange the problem by using the factoring formula identities for and and then simplifying.
Plugging in the values for and gives us the answer of .
Application and Extensions
If , what is the value of ?
The key to solving this problem (without explicitly solving for ) is to recognize that
which gives us
If , what is the value of
This problem is easy once you realize that
The solution is therefore