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Algebraic Expressions Laws

The four basic mathematics operations viz. addition, subtraction, multiplication, and division can also be performed on algebraic equations or expressions. The addition and subtraction of algebraic expressions are almost similar to the addition and subtraction of numbers. However, a combination of variables, constants, and operators constitutes an algebraic expression. But in the case of algebraic expressions, like terms and the unlike terms must be sorted together. The knowledge of like and unlike terms is crucial while studying addition and subtraction of algebraic expressions because the operation of addition and subtraction can only be performed on like terms. The terms whose variables and their exponents are the same are known as like terms and the terms having different variables are unlike terms. Example: -5×2 + 12 xy – 3y + 7×2 + xy In the given algebraic expression, -5×2 and 7×2 are like since both the terms have x2 as the common variable. Similarly, 12xy and xy are like terms

Addition of Algebraic Expressions

There are two methods to add and subtract algebraic expressions, namely the Horizontal Method
and the vertical method. Let us understand these two methods along with the examples in detailed steps.

Horizontal Method

Consider three algebraic expressions 5xy – 3×2 – 12y +5x, xy – 3x – 12yz + 5×3
and y – 6×2 – zy + 5×3.

Step 1: Write the given algebraic expressions using an additional symbol.

(5xy – 3×2 – 12y +5x) + (xy – 3x – 12yz + 5×3) + (y – 6×2 – zy + 5×3)

Step 2: Open the brackets and multiply the signs. 5xy – 3×2 – 12y + 5x + xy – 3x – 12yz + 5×3 + y – 6×2 – zy + 5×3 Step 3: Now, combine the like terms. (5xy + xy) + (-3×2 – 6×2) + (-12y + y) + (5x – 3x) + (-12yz – yz) + (5×3 + 5×3)

Step 4: Add the coefficients. Keep the variables and exponents on the variables the same.

6xy – 9×2 – 11y + 2x – 13yz + 10×3 Column Method In this method,

the given expression must be written column-wise one below the other.

For adding two or more algebraic expressions the like terms of both the expressions are grouped together.

The coefficients of like terms are added together using simple addition techniques and the variable which is common is retained as it is. The unlike terms are retained as it is and the result obtained is the addition of two or more algebraic expressions.

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