Unlock the Algebraic Expressions by simplifying them
- Sep 17, 2017
- Rima Bose
The world of mathematics defines an algebraic expression as an expression that emerges from the integer constants, variables, and the algebraic operations.
Let me simplify it for you. Suppose your teacher has asked you to add 4+ 4+ 4+ 4.
What will you do to solve it quickly?
You will do 4 × 4 that equals to 16, the same answer for the addition of four 4s. You just have to count how many 4s are there, and, then multiply the total number of 4 by 4. Easy, am I right?
Similarly, if you get sums like 6+ 6+ 6+ 6+ 6+ 6+ 6+ 6+ 6+ 6, you need to do 10 × 6. Since there are ten 6s in total; the simplified version is 10 × 6.
You may think, what is the relation between the above examples and algebra?
The primary aspect of solving any algebraic equation is to simplify it. You will be aptly able to make your calculations much easier and save time.
Some necessary steps:-
• Firstly, remove the parentheses by multiplying the factors.
• Use the exponent rules for removing parentheses in terms with the exponents.
• Thirdly, add coefficients and combine like terms.
• Finally, combine the constants.
Watch an example:-
4(3+ a) + 2(4a+6) - (a2)2
While simplifying this equation, the initial thing to study is if you can clear the parentheses. You may utilize the distributive property for clearing parentheses by multiplication of the factors times. Use the distributive property for clearing the first two sets of parentheses.
= 12 + 4a + 8a + 12 - (a2)2
Now, when a term with an exponent becomes a power, you multiply the exponents. Therefore, (a2)2 become a4.
Now, look for the like terms and then combine them. The terms 4a and 8a are like terms as they contains the same variable raised to the same power, that is, the first power, since the exponent is taken as 1.
Combine these two terms and get 12a.
=12 + 12a + 12 - a4
Finally, look for the constants that can be combined. Here, the constants are 12 and another 12. Combine both to get 24.
= 24+12a- a4
Now, you have simplified the whole expression.
Remember one more thing: - We generally write an algebraic expression in a specific order. Start with the terms having the largest exponents. Then, move towards the constants. Use the addition’s cumulative property.
Rearrange the terms. Put the expressions in the right order.
= -a4 + 12a + 24
Therefore, a momentary glance:-
Simplification of Algebraic Equation
If you find the above method a little tight, I have figured out a way to make it easier for you:
If I ask you to simplify: x+ x+ x+ x+ x+ x
Count the numbers of xs’ and multiply the amount by x
You must have got 6 of xs.
Therefore, it will be x +x +x +x +x + x = 6 × x
You can write 6x to simplify it further. Remind that there lies a multiplication between 6 and x.
If you notice minutely, you can see that if you put a 1 next to each x, the answer won’t change.
x+ x+ x+ x+ x+ x= 1x+ 1x + 1x+ 1x+ 1x+ 1x = ( 1 + 1+ 1+ 1+ 1+ 1)x = 6x
You can get two things here:-
1. 1x = x
2. While simplifying the algebraic equation, you can solve the math problem with the number lying on the left of the variable.
Now, try adding x +x +x + x + y + y + y
You cannot add x and y as they are not alike.
You cannot say 2x as there is x + x which is equal to 2x. Nor, you can put 2y as there is y + y that are equal to 2y.
As x and y are different terms, it will be x + y only.
Similarly, x + 2 won’t be 2x. It will be x + 2 only.
You can add all the xs because they are like terms. You can also add the entire ys for the same reason.
So, it will be x + x+ x+ x + y+ y+ y = (x + x+ x+ x) + (y+ y+ y) = 4 × x + 3 x y = 4x + 3y
Let me provide you an expression:-
4x + 3y + 5x + 4y
You have to add 4x and 5x, and, 3y and 4y.
= 4x + 3y + 5x + 4y is equal to 4x +5x + 3y + 4y = 9x +7y
When you will simplify any algebraic expression, putting negative numbers or subtraction works in a similar manner. You have to subtract the like terms. The little difficulty lies in the addition or subtraction of the integers.
4a – 3b – 2a + 4b
It will be 4a – 2a = 2a (the operation on 2a’s left side is a subtraction)
Likewise, in the case of 3b and 4b, you need to change the subtraction to +- as the operation prior to 3b is subtraction.
You will get -3b + 4b = 1b
Therefore, 4a – 3b – 2a + 4b = 2a + 1b
Source: - commons.wikimedia.org
First, look out for the like terms.
See the negative or minus sign lying next to the variables (left side).
Whenever, you have to move the term around, move with the negative sign.
Add or subtract only the integers that are on the left side of the like terms.
Use these guidelines mentioned above to solve your algebraic expression easily and effectively.
Rima is an ardent writer and an awe-inspiring fitness trainer. She surmises in expressing through her mind that has been penned down in her writings. She has maintained her sportsmanship through regular martial arts and swimming. A beautiful mind and a glowing soul shine eternity as per her stance.
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