Let disuse on algebraic simplification and grouping of terms. 3a , 𝓍 + 1 , 7- r and 7 are all examples of algerbraic expressions. In expression 3a , we say that 3 is the coefficient of a. The 3 shows that three a's are added together i mean, 3 x a = a + a + a = 3a we say, a into 3 places.
Also, in 7y is the coefficient of y ; seven y's have been added together.
In x, the coefficient ox is 1 this means 𝓍 x 1 = 𝓍 not 1x
3 𝓍
------------- = 𝓍
3
not 1 𝓍, 3 will go to 3 1 time remainder 𝓍 you should not add the 1.
Note
1.Coefficient are not whole numbers but equations.
2.Coefficient can be fractions. In arithmetic ,
1
------------- x 12
3
are short way of writing ,
1
------------- of 12 or 12 / 3 , which is 4.
3
Also
2a 2 2a
------------- , ---------- is the coefficient of a because ------------ is
3 3 3
2
------------- a .
3
Exerciser 1
What is the coefficient of 𝓍 in the following.
1 .13𝓍
1
2. -------- 𝓍
2
Solution
1. we say 13 x 𝓍 = 𝓍 + 𝓍 + 𝓍 +......... in to 13 places = 13𝓍 ,
13 is the coefficient of 𝓍.
1
2. -------- 𝓍
2
1 𝓍
= ------------ x --------
2 1
1 x 𝓍 𝓍 1
= ----------- = ------- = ------
2 x 1 2 2
is the coefficient of 𝓍
Grouping of positive and Negative Terms
3𝓍 + 2𝓍 means 3 𝓍 add to 2𝓍, that will bring 5𝓍 . we it this way,
3𝓍 + 2𝓍 = 5𝓍. There are like terms.
6y - 2y = 4y
Examples
Simplify the following
1. 7𝓍 + 2𝓍 - 4𝓍
= 7𝓍 + 2𝓍 - 4𝓍
= ( 7𝓍 + 2𝓍)- 4𝓍 -- according to the rule of BOD-MAS
= 9𝓍 - 4𝓍
= 5𝓍
2. 8𝓍 - c + 3c
= 8𝓍 - ( c + 3c)
= 8𝓍 - 4c -- 𝓍 and c are unlike term
3.Simplify 4b + 2b - 9b + 8b
= ( 4b + 2b ) - 9b + 8b
= 6b - b
= 5b
If you look at the last expression, you'll see that 4 will add 2 and 9 will minus 8 to become 1b you will note include the 1 but b only.
Now solve these
Simplify the following
1. 20c - 9c - c + 2c
2. 12d - 5d - 3d + 4d
3. 17p - 8p - 2m
Now if you have any question concerning the above examples, please put them in the comment box.
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