Algebraic Expressions and Identities Class 8 Notes is specially designed to help students understand important chapter concepts clearly and study productively. These notes will also enable students to have an effective math practice session and be ready to tackle chapter questions that could be asked in the exams. Besides, some of the key topics covered in the notes include;
- What are Expressions?
- Terms, Factors and Coefficients.
- Monomials, Binomials and Polynomials.
- Addition and subtraction of algebraic expressions
- Multiplication of Algebraic Expressions.
- Standard Identities
- Important Questions
What are Algebraic Expressions?
Algebraic expressions are nothing but expressions that usually contain constants, variables, and operations like addition, subtraction, multiplication, division, etc by an exponent which is a rational number. For example; x + 3, 2y – 5, 3×2, 4xy + 7.
Terms, Factors and Coefficients
- A term is said to be either a single number or a variable. Furthermore, it can also be a combination of numbers and variables. Terms are generally separated by different operators like +, -, or others.
The terms which have the same variables are known as like terms. Example: 2xy and 3yx. The terms with different variables are known as unlike terms. Example: 2xy and 3ax.
- The product of numbers or number and variable are known as Factors.
- A coefficient is the number multiplied to a variable.
Monomials, Binomials, Trinomial and Polynomials
Addition and Subtraction of Algebraic Expressions
When we need to add algebraic expressions the like terms of both the expressions are grouped together. Then the coefficients of like terms are added together while the common variable is retained as it is. Whereas, the unlike terms remain as it is.
As for subtracting two or more algebraic expressions, it is good practice to place the expression to be subtracted below the expression to be subtracted from and generally, like terms are placed below each other. However, in doing this, the sign of each term is reversed and the resulting expression is added.
Multiplication of Algebraic Expressions
When we talk about the multiplication of algebraic expressions it is actually quite different than ordinary multiplication process. Multiplying algebraic expressions usually involves multiplying variables and constants separately and in different ways. There are also few key things to remember when calculating like and unlike terms.
For like terms:
- Coefficients get multiplied.
- The power of the resultant variable is the sum of the individual powers.
For unlike terms:
- Coefficients also get multiplied.
- There will be no change in the power of variables if all the variables are different.
- Some power of variables is added if few of the variables are same.
In general, identity is standard equality which is true for all the values of the variables in the equality. Some of the different standard identities are given in the table below.
|Identity I||(a + b)2 = a2 + 2ab + b2|
|Identity II||(a – b)2 = a2– 2ab + b2|
|Identity III||(a + b)(a – b) = a2 – b2|
|Identity IV||(x + a)(x + b) = x2 + (a + b) x + ab|
Notably, these four identities are used in calculating squares and products of algebraic expressions. They are also used to calculate products of numbers and other problems.
- Give 3 examples of expressions containing a variable and 3 examples of expressions containing more than one variable.
- Classify the given polynomials as binomials, trinomials and monomials.
i.x + 4, ii. a+b+c, iii. B+c+100 iv. xy – xz
- Factorize (x2 + 8y3 + 27z3 – 18xyz) using standard algebraic identities.