Introduction to Algebraic Expressions
Before we move to Algebraic expression first have a look on basic concept of algebra. Algebra is that mathematical branch that mainly deals with number, variables and different operations on it. Algebraic expressions are formed using variables and constants. In mathematical term it can be defined as a combination of the finite symbols that are formed according to rules of the context. The algebraic expression is used to designate the value for the given variables in the expression. The expression may or may not be depending on the values assigned to the variables in the expression. The expression is the syntactic concept in the algebra.
Let’s have example as example is the best way to understand the concept and grasp important points and way to solve the problems.
Example 1: a2+ 56a+ 768.
Output: The given expression is a2+ 56a+ 768.
=> a2+ 56a+ 768 = a2+24a+ 32a+ (24x 32)
=> a2+ 56a+ 768 = a(a+24) + 32(a +24)
=> a2+ 56a+ 768 = (a+24) (a+32)
=> a+24 and a+32
The factors for the given expression a2+ 56a+ 768 are (a +24) and (a +32).
Example 2: simplify the algebraic expression given as: y2+ 76y+ 1440.
Answer: The given expression is y2+ 76y+ 1440.
y2+ 76y+ 1440 = y2+36y+ 40y+ (36x 40)
y2+ 76y+ 1440 = y(y+36) + 40(y +36)
y2+ 76y+ 1440 = (y+36) (y+40)
y+36 and y+40
The factors for the given expression y2+ 76y+ 1440 are (y +36) and (y +40).
These are the Algebraic expression in the form of equations. When you deal with algebraic expression you also deal with word problems and have to form an expression from the given problems. Whenever you deal with word problems, analyze the problem, understand the problem, note what is given and what not and form the relevant expression or equation. Let’s have an example of this; Jay has $17 in his account. how much money does he need to buy a game that costs $68?
Solution: Suppose ‘x’ represents the amount of money Jay needs. Then the following equation can represent this problem as:
17 + x = 68,
To solve this we can subtract 17 from both sides of the equation to get the value of the ‘x’,
68 – 17 = x,
x = 51, so Jay needs $51 to buy the new game.
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