Here in this post, i will teach how to simplification in algebra term.When i mean term, the like and the unlike terms.Simplification simply talk about grouping numbers and their coefficient in one expression which can be simplified the same same kind together You only need attention before you can get the whole concept. Mathematics is very simply, to some , but others is very hard.Here I break it down to your understanding.
Example 1
Simplify 7a - 2a - 9a + 10a
It is said to to be by grouping positive and negative terms together,
7a - 2a - 9a + 10a
= 7a + 10a - 2a - 9a
= 17a - 11a
= 6a
Also by treating the terms as directed numbers only,
9a - 5a - 8a + 10a
= 4a - 8a + 10a
= - 4a + 10a
= 6a
There are two ways you can do that , using addition first before subtraction, or by treating the terms as directed numbers.
Example 2
Simplify 5x -8x + x + 3y
5x -8x + x + 3y
= -3x + x + 3y
= -2x + 3y
In the above examples, note that 2x and 3y are unlike terms .3y -2x cannot be simplified any further.
Bracket
Now, we will solve some algebraic expression that involved opening the bracket.If any quantity multiplies the terms inside a bracket, every term inside the bracket must be multiplied by that quantity when the bracket is removed.
As we all know, a(x + y) = ax + ay
also, a(x - y) = ax - ay
Example 3
Remove the bracket from 4(3x - 5y + z )
4(3x - 5y + z )
= 4 x 3x - 4 x 5y + 4 x z
= 12x - 20y + 4z
Note: Since the last terms are not in the same like, so cannot simplify the further.They are called unlike terms.
Example 4
Remove bracket and simplify 4 - ( a - 5 - 6a )
4 - ( a - 5 +6a )
= 4 - ( a - 5 + 6a )
= 4- ( 7a - 5 )
= 4- 7a + 5
Rearrange to add 4 and 5.
= 4 + 5 - 7a
= 9- 7a
In the above example ,notice that the inner bracket is removed first . Notice also that a negative sign outside a bracket is equivalent to -1 outside the bracket .
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