Here in the post you will learn a lot based on algebraic terms, I will teach you how to solve problems related to algebraic expression with full guides. Algebraic is that branch of mathematics that involve numbers and letters.
Evaluating an expression simply means substituting known numbers in place of the variables and calculating the final numerical value using the standard Order of Operations (PEMDAS/BODMAS). The most critical pitfall here is handling negative bases with exponents. Students frequently write. However, substituting a negative number requires enclosing it in parentheses
If you're having problem on how to work on this topic, brainimatic Series will show you what to do when asked to simplify algebraic expression. But first, you must be familiar with the the rule of BODMAS, because algebraic expression some signs.
Also, collecting like term is also involve in this operation.Now I will solve some examples of algebraic expressions, you just need to pay attention and also do yours the way I'm solving mine.
Example 1
Simplify (3x + 5y - x + 2y)
Solution
First let bring out the equation from the bracket.
= 3x + 5y - x + 2y
Collect like term
= 3x - x + 5y + 2y
= 2x + 7y
This is simple, the 3x and x itself are liked terms. While 5y and 2y are also liked terms.
Group the x terms together: 3x - x
Group the y terms together: 5y + 2y
Another thing you should consider is the sign, the x that has negative signed, while the 5y has addition sign. This means, when ever a term is moving, the term should move with the sign. I hope it's well clear.
2. Evaluate 2a² - 3b when a = 3 and b = -2
Solution
Evaluation requires substituting the given numerical values into the variables of the expression and following the order of operations (BODMAS).
Now the first thing to do is to substitute a for 3 , and b for -2
= 2a² - 3b
= 2 x 3² - (3 x -2 )
= (2 x 9) - ( - 6 )
= 18 + 6
= 24
That's amazing working, this involves substitution for a and b for their value to take place. We just separate the terms this way:
2a²
And
3b
So that we can work it out, we multiply minus and minus that give us plus,then we add them altogether. When you're ask to solve such similar question, use this Brainimatic Series and you're good to go...
3.Expand the expression 4(2x - 7)
To expand this expression, apply the distributive property, which states that You must multiply the term outside the parentheses by every term inside the parentheses.
Solution
4(2x - 7)
Multiply 4 by 2x and -7 to open the bracket
= 8x - 28
4.Siplify 2( 3x + 4) - 3(x - 2)
Solution
In this one, we will first open the left hand side bracket , then the right hand side
= 2( 3x + 4) - 3(x - 2)
= 6x + 8 - 3x + 6
Collect like term
= 6x - 3x + 8 + 6
= 3x + 14
Yes that amazing explanation! Now, you take a look at the above information, to work on the question above, we open the left hand of the bracket, to open any bracket in mathematics, we multiply outside variables with inside variables. Another thing you should always remember is immediately you are at the right side, always multiply the sign
- 3(x - 2)
-3x + 6
Minus multiply by minus that will give us plus.
x² - 9
5. Simplify -----------------
x² + 5x + 6
Explanation:To simplify a fraction containing algebraic expressions, you must factor both the numerator and the denominator completely and cancel out common factors.
Then we do it this way:
Numerator x² - 9 ( difference of 2 squares)
( x - 3)( x + 3)
Denominator x² + 5x + 6 ( find the sum and the product)
First find the products of 6.
1 x 6 = 6
2 x 3 = 6 ------ is good for the operation
Sum ---- 2 +3 = 5
Product ----- 2 x 3= 6
Now we have:
x² - 9
-----------------
x² + 5x + 6
( x - 3)( x + 3)
= --------------------------
x² + 2x + 3x + 6
( x - 3)( x + 3)
= ----------------------------
( x + 2)( x + 3)
Now let's council the same term ( x + 3 )
( x - 3 )
= ---------------
( x + 2 )
Remember to factor the numerator and denominator if you have the above similar problem.
6.Simplify ( 2x - 3 )²
Solution
Now in the issue, we multiply the same equation into two places with the bracket
( 2x - 3 ) by its self because
n² means n x n..
= ( 2x - 3 )( 2x - 3 )
= 2x( 2x - 3 ) - 3( 2x - 3 )
= 4x² - 6x - 6x + 9
= 4x² -12 + 9
Yeahhhh, this is really good. Now let brainimatic Series explain , please if you're a student or you just love mathematics, I encourage you to read use AI for further explanation. The mathematical questions above is very simple to solve but it's need concentration. Let's go oooo.
First, n square is n² = n x n
So what about ( 2x - 3 )² , it's the same thing as ( 2x - 3 )( 2x - 3 )
Also 3² means 3 x 3 = 9
Before we open the bracket
Now solve the following:
1. ( 2x + 1)²
x² - 4
2. --------------
(2x - 4)²
3. (2x - 3 ) - ( 3x + 4)
With Brainimatic Series lesson, you should be able to solve the above questions. Visit this page for more understanding, thank you for your attention. If you have any question put them in the comments box.
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