Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Important Formulas: Algebraic Expressions & Identities
Important Formulas: Algebraic Expressions & Identities | Mathematics (Maths) Class 8 PDF Download
Algebraic expression is the expression having constants and variable. It can have multiple variable and multiple power of the variable
Example:
- 11x
- 2y – 3
- 2x + y
Some Important points on Algebraic expressions
1. Terms
Terms are added to form expressions
2. Factors
Terms themselves can be formed as the product of factors
3. Coefficient
The numerical factor of a term is called its numerical coefficient or simply coefficient.
4. Monomial
Algebraic expression having one terms is called monomials
Example: 3x
5. Binomial
Algebraic expression having two terms is called Binomial
Example: 3x+y
Question for Important Formulas: Algebraic Expressions & IdentitiesTry yourself:Which term in the given algebraic expression is a binomial?
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6. Trinomial
Algebraic expression having three terms is called Trinomial
Example: 3x+y+z
7. Polynomial: An expression containing, one or more terms with non-zero coefficient (with variables having non negative exponents) is called a polynomial.
8. Like Terms: When the variable part of the terms is same, they are called like terms
9. Unlike Terms: When the variable part of the terms is not same, they are called unlike terms.
Operation on Algebraic Expressions
1. Addition
(a) We write each expression to be added in a separate row. While doing so we write like terms one below the other
Or
We add the expression together on the same line and arrange the like term together
(b) Add the like terms
(c) Write the Final algebraic expression
2. Subtraction
(a) We write each expression to be subtracted in a separate row. While doing so we write like terms one below the other and then we change the sign of the expression which is to be subtracted i.e. + becomes – and – becomes +
Or
We subtract the expression together on the same line, change the sign of all the term which is to be subtracted and then arrange the like term together
(b) Add the like terms
(c) Write the Final algebraic expression
3. Multiplication
(a) We have to use distributive law and distribute each term of the first polynomial to every term of the second polynomial.
(b) when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents
(c) Also as we already know ++ equals =, +- or -+ equals - and -- equals +
(d) group like terms
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FAQs on Important Formulas: Algebraic Expressions & Identities - Mathematics (Maths) Class 8
| 1. What are the basic algebraic identities that every student should know? |  |
Ans. The basic algebraic identities include:
1. $(a + b)^2 = a^2 + 2ab + b^2$
2. $(a - b)^2 = a^2 - 2ab + b^2$
3. $a^2 - b^2 = (a + b)(a - b)$
4. $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$
5. $(x + y + z)^3 = x^3 + y^3 + z^3 + 3(x+y)(y+z)(z+x)$
| 2. How can I simplify algebraic expressions using identities? | |
Ans. To simplify algebraic expressions using identities, identify the form of the expression you have. For instance, if you have $(a + b)^2$, you can replace it with $a^2 + 2ab + b^2$. Use the relevant identity that matches the structure of the expression to rewrite it in a simpler form.
| 3. What is the significance of studying algebraic identities in mathematics? | |
Ans. Studying algebraic identities is crucial in mathematics as they provide tools for simplifying complex expressions, solving equations, and proving other mathematical concepts. They also enhance problem-solving skills and are widely applicable in higher-level mathematics, physics, and engineering.
| 4. Can you provide examples of how to apply algebraic identities in solving equations? | |
Ans. Certainly! For example, if you need to solve the equation $x^2 - 9 = 0$, you can recognize that it fits the identity $a^2 - b^2 = (a + b)(a - b)$. Here, $a = x$ and $b = 3$, so you can factor it as $(x + 3)(x - 3) = 0$. This gives the solutions $x = -3$ and $x = 3$.
| 5. What are some common mistakes to avoid when working with algebraic expressions and identities? | |
Ans. Common mistakes include:
1. Misapplying identities, such as confusing $(a + b)^2$ with $a^2 + b^2$.
2. Failing to expand expressions correctly, leading to incorrect simplifications.
3. Not keeping track of negative signs, especially when using subtraction in identities.
4. Forgetting to apply the identity thoroughly, which can lead to incomplete or inaccurate answers.
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