Eduki

The process of transforming an expression within the rules of mathematical operations or properties is known as symbolic transformation. Expressions obtained by such transformations are such that replacing the value of a variable with any number will satisfy both sides. For example, 𝑥+𝑥+𝑥 can be written as 3𝑥 using the distributive property. 

Suppose 𝑥 is taken to be 25, then 25+25+25 is also 75 and 3*25 is also 75.

If 𝑥 is 3 then 3+3+3 is also 9 and 3*3 is also 9

Putting any value in place of 𝑥 in both 3𝑥 and 𝑥+𝑥+𝑥 will give the same result and thus they are equivalent expressions. 

Equivalent expressions

The distributive property is the property by which expressions under multiplication/division can be written in the form of addition/subtraction. 

For example, a(b+c)=ab+ac

(𝑥+z)/y=(𝑥/y) + (z/y)

The commutative property is another property that helps in finding equivalent expressions. The commutative property is valid in a lot of operations such as addition and multiplication whereas is invalid for operations such as subtraction and division. a+b is the same as b+a whereas a-b isn't the same as b-a. In a similar way, a*b is equal to b*a whereas a/b is not equal to b/a. The statements may sound obvious, but they are very useful while performing symbolic transformations on algebraic expressions. 

If two expressions give the same value for only some of the numbers, then such expressions aren't equivalent to each other. 5𝑥 and 𝑥-8 give equal values only when 𝑥 = -2, at all other values for 𝑥 these two expressions give different values. So, these expressions can't be termed as equivalent. 

Indices

In the acronym PEMDAS, E stands for exponents. Let's learn a few things about how to work with exponents. If a number has to be multiplied to itself many times, then exponents are used. For example, 25^2 means 25 multiplied by itself twice i.e. 25 x 25. 25^3 means 25 x 25 x 25.

The area of the square is given by the square of its length, so the “a” has to be multiplied twice. a x a can be written as a^2. Here 2 is written as an index to show how many times “a” has to be multiplied. The operation between indices follows some rules that are known as the laws of indices. 

In the same manner, the volume of a cube with side length “a” is denoted by a^3, which means that the length of the cube has to be multiplied 3 times.