Algebra is one of the interesting and real-life applications that use symbols and letters to represent numbers, but how is it possible to replace a number with letters or symbols when both of these are different things? Algebra is something where we assign variables to understand relationships between values in a given statement. It uses four mathematical operations, such as addition, subtraction, multiplication, and division. Well, let us consider a scenario of two sisters Mary and Sherry, where Mary is three years younger than twice the age of Sherry, so how to represent this in mathematical terms?
We will cover all these conceptions on our page along with interesting formulas as algebra revolves around equations and formulas.
For instance, we have 8 + 9 = p and we know the value of x after performing addition will be 17, so x is just a blank or a placeholder to put a value in. Also, 8 and 9 are known values, and ‘p’ (a symbol) is unknown. This statement embarks on the concept of “Algebraic Equations.”
What are Algebraic Equations?
From the above text, we understand that in Algebra, our goal is to find the “unknown,” and when doing this, we call it “solving the equation.”
For instance, a man is two inches taller than thrice the height of a lady, so how do we represent this statement?
Well, here we have a man as “A” and a lady as “B”, and
A is thrice the height of B, i.e., A = 3B
Also, A is 2 inches taller, so A = 3B + 2…(1), is our required equation
Here, instead of using words, we minimalized our efforts by using eq (1). Now, consider the height of B as 4 inches. So, we get the height of A by putting the value of B in eq (1): A = 3 * 4 + 2 = 14 inches. Therefore, the height of A is 14 inches.
Similarly, we can find infinite values of a height by just putting various values in eq (1).
Now, let us consider an equation to understand algebra a bit more.
Examples of Algebraic Formulas
Example 1: Suppose a woman is 25 years of age and her son is 4 years of age, so what is their age difference?
Solution: Now, here, we notice that woman “w” = 25 and son “s” = 4, so their difference: 25 – 4 = 21 years. Now, let us break down this problem in a simpler manner:
Here, 25 = 52 and 4 = 22
We write 52 – 22 = (5 + 2) (5 – 2)
=> 5 + 2 = 7 and 5 – 2 = 3
So, 7 * 3 = 21 is the age difference that we obtained above.
We obtain our algebraic formulas in the following manner:
p2 – q2 = (p +q) * (p-q) ….(1)
Example 2: Let’s say A is 125 cm tall and 64 cm tall, the difference of their heights will be 125 – 64 = 61 cm simply. Now, let us relate these values in the following algebraic expression:
125 = p or p3 = 53
Similarly, q3 = 43
Or, p3 – q3 can be written in the new format as:
p3 – b3 = (p – q) * (p2 + pq + q2)
= (5 – 4) * (52 + 5 * 4 + 42)
Therefore, we get 1 * (61) = 61 years
Algebraic Formula Chart
Mentioned below are a few algebra formulas that is used to solve different mathematical problems:
| (p + q)2 | p2 + 2pq + q2 |
| (p – bq | p2 – 2pq + q2 |
| (p + q + r)2 | p2 + q2 +r2 +2pq + 2qr + 2pr |
| (p – q – r)2 | p2 + q2 +r2 -2pq + 2qr – 2pr |
In the above examples, we understood how to represent real-life scenarios in the form of variables and the relationship between those two. The Algebraic Formula Chart provides the relationship between two or more values from simpler to complex expressions. You can use these formulas to apply these in your questions. You may learn more about algebra formulas through Cuemath’s online classes. Visit the website for more information.