RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6.4

Adding algebraic expression consist of  step by step procedure, they are listed below:

• Step 1: Sort out all the like terms based on the variables, i.e., group all the same variable terms.

• Step 2: Perform addition on all the grouped terms with the same variables by adding the coefficients and should be written in a single coefficient term.

• Step 3: Similarly, perform operations for all the like terms.

• Step 4: The addition of constants should be done like the usual addition of numbers.

• Step 5: If no like terms are present, then keep the expression as it is.

In the multiplication of algebraic expressions, there are two simple rules,

(i) The product of two terms with like (same) signs are positive. The product of two terms with unlike (different) signs are negative.

(ii) If x is a variable and m, n are positive integers, then (x^m×xⁿ)=x^m+n.

Following are the steps for multiplication of algebraic expressions:

• Step 1: Multiply each term of the first expression with each term of the second expression.

• Step 2: If the same variables appear, add the powers and express them as exponents with the variable.

• Step 3: Write as the product of another variable, if there are different variables.

• Step 4: After Multiplication separate every term obtained by its respective signs.

The following are some of the important algebraic identities

• a² − b²= (a - b) (a + b)

• (a + b)²= a² + 2ab + b²

• (a - b)²= a² − 2ab + b²

• (a + b + c)²= a² + b² + c² + 2ab+ 2bc + 2ca

• (a + b)³= a³ + 3a²b + 3ab² + b³ = a³ + b³ + 3ab (a + b)

• (a - b)³= a³ − 3a²b + 3ab² − b³ = a³ − b³ − 3ab ((a - b)

• a³ − b³= (a - b) (a² + ab + b²)

• a³ + b³= (a + b) (a² − ab + b²)

• a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc− ca)