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December 25, 201539 Insightful Publications

**Algebra Formulas for Class 8: **The compiled Algebra formulas and Algebraic identities here in this article will help all Class 8 students in their studies and final exams. Algebra is a broad part of Mathematics in which we study mathematical symbols and the rules for manipulating these symbols. Different symbols and letters are used to represent quantities and numbers.

Algebra has many real-life applications in mathematics, science, engineering, medicine, and economics. Algebraic identities for Class 8 and algebraic expressions are introduced in the CBSE curriculum. As it is one of the most important units for CBSE Class 8, we have provided the complete list of important Math formulas for Class 8 Algebra on this page. Scroll down to read more.

Students who are looking for the complete list of maths formulas for Class 8 PDF for algebra can refer to this article. You can check the list in the table below:

1. a^{2} – b^{2} = (a – b)(a + b)2. (a + b) ^{2} = a^{2} + 2ab + b^{2}3. a ^{2} + b^{2} = (a + b)^{2} – 2ab4. (a – b) ^{2} = a^{2} – 2ab + b^{2}5. (a + b) ^{3 }= a^{3 }+ b^{3 }+ 3ab(a + b)6. (a – b) ^{3 }= a^{3 }– b^{3 }– 3ab(a – b)7. a ^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})8. a ^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})9. x(a + b) = xa + xb 10. x(a – b) = xa – xb 11. (x – a)(x – b) = x ^{2 }– (a + b)x + ab12. (x – a)(x + b) = x ^{2 }+ (b – a)x – ab13. (x + a)(x – b)= x ^{2 }+ (a – b)x –ab14. (x + a)(x + b)= x ^{2} + (a + b)x + ab15. (x + y + z) ^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2zx16. (x – y – z) ^{2} = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2zx |

Almost all of the **Class 8 Maths NCERT Solutions** for algebra units can be done using these formulas.

Get a detailed Math formula chart for Class 8, including Trigonometry, Mensuration, Profit & Loss, Probability, and Exponents below:

An algebraic identity is an equality that holds for any values of variables. So, if we know the values to the left of an expression, we can deduce the result using the algebraic identity. An algebraic expression contains two things – Variables and Constants. The value of the variable changes in different expressions while the constant remains the same.

**Important Points Regarding Algebraic Expressions Formulas**

- A variable can take any value. The value of expression changes with the value chosen for its variables.
- A line has an infinite number of points. A variable can take any position on the number line.
- There are different types of algebraic expressions depending on the number of terms they contain: expressions containing one, two and three terms are called monomial, binomial and trinomial expressions.
- The numerical factor of a term is called its coefficient.
- An identity is standard equality which is true for all the values of the variables in the equality.

Understand different algebraic identities for Class 8 with examples provided below. These examples will help you memorise the Class 8 algebra formula we provided above.

**1) Find out the value of 5 ^{2} – 3^{2}**.

Since a

5

= (5 + 3)(5 – 3)

= 8 x 2

= 16.

Hence, the answer is 16.

**2) 4 ^{3} × 4^{2} =?**

Since (a

4

= 4

= 4

= 1024.

Hence, the answer is 1024.

**3) Evaluate the value of (95) ^{2} using identities.**

This can be expressed as (a-b)

Since (a-b)

95

= (100-5)

= 100

= 10000 – 1000 + 25

= 9025.

Hence, the answer is 9025.

**4) What is the value of x**^{2}** + y**^{2}** – 10 at x = 0 and y = 0?****Solution**: x^{2} + y^{2} – 10,

Putting x = 0 and y = 0 in the expression, we get:

0^{2} + 0^{2 }– 10

= 0 – 10

= -10

Hence, the answer is -10.

**5) Simplify (a + b + c)(a + b – c)****Solution: **Using the algebraic expression: x(a+b) = xa + xb, we can simplify the equation as follows:

(a+b+c)(a+b-c)

= a(a+b-c) +b(a+b-c) +c(a+b-c)

= axa + axb – axc + bxa + bxb – bxc + cxa + cxb – cxc

= a^{2} + ab – ac + ba + b^{2} – bc + ca + cb – c^{2}

= a^{2} + b^{2} – c^{2} + ab + ba + ca – ac – bc + cb

= a^{2} + b^{2} – c^{2} + 2ab

Now that we have provided algebraic formulas for Class 8 with examples let’s practice some important questions related to algebraic formulas and expressions.

Here we have provided some practise questions on the Algebra chapter for CBSE Class 8. These questions will brush up your concepts and help you memorise the algebra formula we provided above.

**Question 1: Classify the following polynomials as monomials, binomials, and trinomials. Which polynomials do not fit in any category?**

(i) x+y | (ii) 1000 |

(iii) x+x ^{2}+x^{3}+x^{4} | (iv) 7+a+5b |

(v) 2b-3b ^{2} | (vi) 2y-3y ^{2}+4y^{3} |

(vii) 5x-4y+3x | (viii) 4a-15a ^{2} |

(ix) xy+yz+zt+tx | (x) pqr |

(xi) p ^{2}q+pq^{2} | (xii) 2p+2q |

**Question 2: Find each of the following products:**

5x^{2} × 4x^{3} | -3a ^{2} × 4b^{4} |

1/2xy × 2/3x ^{2}yz^{2} | (-7xy) × (1/4x ^{2}yz) |

2a ^{3 }(3a + 5b) | -11y ^{2 }(3y + 7) |

xy (x ^{3} – y^{3}) | 0.1y (0.1x ^{5} + 0.1y) |

4/3a (a ^{2} + b^{2} – 3c^{2}) | 1.5x (10x ^{2}y – 100xy^{2}) |

**Question 3: Multiply the monomial by the binomial and find the value of each for x = -1, y = 0.25, and z = 0.005:(i) 15y ^{2} (2 – 3x)(ii) -3x (y^{2 }+ z^{2})(iii) z^{2} (x – y)(iv) xz (x^{2} + y^{2})**

**Question 4: Simplify:**

**(i) 2x ^{2}(x^{3} – x) – 3x(x^{4} + 2x) – 2(x^{4} – 3x^{2})**

**(ii) x ^{3}y(x^{2} – 2x) + 2xy(x^{3} – x^{4})**

**(iii) 3a ^{2} + 2(a+2) – 3a(2a+1)**

**(iv) x(x+4) + 3x(2x ^{2} -1) + 4x^{2} + 4**

**(v) a(b-c) – b(c-a) – c(a-b)**

**Question 5: Using the formula for squaring a binomial, evaluate the following:**

**(i) (102) ^{2}**

**(ii) (99) ^{2}**

**(iii) (1001) ^{2}**

**(iv) (999) ^{2}**

**(v) (703) ^{2}**

**Q1: Why is Algebra considered important in Mathematics?Ans: **Algebra is one of the most important branches of Mathematics, along with Number Theory, Geometry and Analysis. The concepts of Algebra are crucial to understanding the theory of Partial Differential Equations. Apart from that, algebra is crucial in physical systems such as movement and forces, heat transfers, and so on.

**Q2: What are the different components of the Algebra formulas and expressions?Ans: **Algebra formulas and expressions can be divided into the following components:

1. Algebraic Identities

2. Laws of Exponent

3. Quadratic Equations

4. Other Important Expressions

**Q3: What is the difference between Algebra and Arithmetic?Ans:** Algebra uses letters to represent either unknown or allowed to take on many values. On the other hand, arithmetic is all about computing specific numbers. Arithmetic consists of simple operations like division, multiplication, addition and subtraction, whereas Algebra is the Math of finding unknown values in an equation with the help of variables.

**Q4: What does the word ‘algebra’ mean?Ans:** The word ‘algebra’ has several related meanings in Mathematics. When used as a single word, it means ‘a broad part of mathematics’. Algebra can also be used with qualifiers like linear algebra, elementary algebra, modern algebra, and so on.

**Q5: What are the types of rules in Algebra?Ans: **The types of rules in algebra are as follows:

1. Commutative Rule of Addition.

2. Commutative Rule of Multiplication.

3. Associative Rule of Addition.

4. Associative Rule of Multiplication.

5. Distributive Rule of Multiplication.

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