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Algebra Formulas for Class 9: Algebra is a branch of mathematics in which universal symbols and letters are used to represent quantities and numbers in equations and formulas. Algebra is divided into two sections: Elementary Algebra and Modern Algebra (Abstract Algebra). Algebraic expressions formulas for Class 9 have been included in the CBSE curriculum so that students may comprehend the value of Algebra in their daily lives.
In CBSE Class 9, the chapter on algebraic expressions and identities is introduced. Algebra is one of the most straightforward and high-scoring topics. However, if you do not recall different Maths formulas for Class 9 Algebra and how to use them in Algebraic Expressions and identities, it can be a challenge. To make it easier for students, we have included algebraic equations examples with answers on this page. Continue reading to know more.
Students who are looking for the complete list of Maths formulas for Class 9 Algebra can refer to the table:
|1. (a + b)2 = a2 + 2ab + b2|
2. (a − b)2 = a2 − 2ab + b2
3. (a + b)(a – b) = a2 – b2
4. (x + a)(x + b) = x2 + (a + b)x + ab
5. (x + a)(x – b) = x2 + (a – b)x – ab
6. (x – a)(x + b) = x2 + (b – a)x – ab
7. (x–a)(x–b) = x2 – (a+b)x + ab
8. (a + b)3 = a3 + b3 + 3ab(a + b)
9. (a – b)3 = a3 – b3 – 3ab(a – b)
10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz − xz)
15. x2 + y2 = 12[(x + y)2 + (x – y)2]
16. (x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
17. x3 + y3 = (x + y)(x2 – xy + y2)
18. x3 – y3 = (x – y)(x2 + xy + y2)
19. x2 + y2 + z2 − xy – yz –zx = 1/2[(x − y)2 + (y − z)2 + (z − x)2]
Do you know the difference between an algebraic formula (identity) and an algebraic expression? An algebraic formula is an equation that is a rule written using mathematical and algebraic symbols. It always involves algebraic expressions on both sides. Moreover, equality will hold true for any values of variables.
On the other hand, an algebraic expression is not separated by an equal sign. An algebraic expression contains two things – Variables and Constants. The value of the variable changes in different expressions while the constant remains the same. We can understand the difference between the two from the following example:
(a + b)2 =a2 + 2ab + b2 is an algebraic formula and here,
(a + b)2 is an algebraic expression.
a2+ 2ab + b2 is an algebraic expression.
The LHS and RHS of an algebraic formula are always equal for any value of the variables in it. This property allows us to deduce the result on RHS if we know the values to the left of an expression.
Check out other important Maths articles for Class 9:
|NCERT Solutions for Class 9 Maths||Class 9 Maths Syllabus|
|NCERT Books for Class 9 Maths||Maths Formulas for Class 9|
Now that we have provided all Algebra formulas for Class 9, let’s see some examples of the same:
|Question 1: Evaluate each of the following using identities:|
(i) (2x – 1/x)2
(ii) (2x + y) (2x – y)
Answer: (i) (2x – 1/x)2
Using identity: (a – b)2 = a2 + b2 – 2ab, we get:
(2x – 1/x)2
= (2x)2 + (1/x)2 – 2 (2x)(1/x)
= 4x2 + 1/x2 – 4
(ii) (2x + y) (2x – y)
Using identity: (a – b)(a + b) = a2 – b2, we get:
(2x + y) (2x – y)
= (2x )2 – (y)2
= 4x2 – y2
|Question 2: Simplify the following:|
(i) 175 x 175 +2 x 175 x 25 + 25 x 25
(ii) 322 x 322 – 2 x 322 x 22 + 22 x 22
Answer: (i) Using identity: a2+ b2+2ab = (a+b)2, we get:
175 x 175 +2 x 175 x 25 + 25 x 25
= (175)2 + 2 (175) (25) + (25)2
= (175 + 25)2
(ii) Using identity: a2+ b2-2ab = (a-b)2, we get:
322 x 322 – 2 x 322 x 22 + 22 x 22
= (322)2 – 2 x 322 x 22 + (22)2
= (322 – 22)2
|Question 3: If m + 1/m = 11, find the value of m2 +1/m2. |
Answer: m + 1/m = 11 (Given)
So, (m+1/m)2 = m2 + 1/m2 + 2 x m x 1/m
⟹ (m+1/m)2 = m2 + 1/m2 + 2
⟹ (11)2 = m2 + 1/m2 + 2
⟹ 121 = m2 +1/m2 + 2
⟹ m2 +1/m2 = 119
|Question 4: Write the following in the expanded form: |
(i) (a + 2b + c)2
(ii) (a2 +b2 +c2) 2
(iii) (a/bc + b/ac + c/ab) 2
Answer: Using identity: (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz, we can expand the algebraic expressions.
(i) (a + 2b + c)2
= a2 + (2b) 2 + c2 + 2a(2b) + 2ac + 2(2b)c
= a2 + 4b2 + c2 + 4ab + 2ac + 4bc
(ii) (a2 +b2 +c2) 2
= (a2) 2 + (b2) 2 + (c2 ) 2 + 2a2 b2 + 2b2c2 + 2a2c2
= a4 + b4 + c4 + 2a2 b2 + 2b2 c2 + 2c2 a2
(iii) (a/bc + b/ac + c/ab)2
= (a/bc)2 + (b/ac)2 + (c/ab)2 + 2(a/bc)(b/ac) + 2(b/ac)(c/ab) + 2(c/ab)(a/bc)
= a2/b2c2 + b2/c2a2 + c2/a2b2 + 2/a2 + 2/b2 + 2/c2
Here we have provided some of the practice questions on Algebraic expressions formulas for Class 9:
Question 1: Factorize the following algebraic expressions:
(i) x3 + x – 3x2 – 3
(ii) a(a + b)3 – 3a2b(a + b)
(iii) x(x3 – y3) + 3xy(x – y)
(iv) a2x2 + (ax2 +1)x + a
Question 2: What are the possible expressions for the dimensions of the cuboid whose volume is 3x2 – 12x.
Question 3: Resolve into factors for the following algebraic expressions:
(i) (x + 2)(x2 + 25) – 10x2 – 20x
(ii) 2a2 + 26–√ ab +3b2
(iii) a2 + b2 + 2(ab + bc + ca)
(iv) 4(x – y)2 – 12(x -y)(x + y) + 9(x + y)2
Question 4: Find the H.C.F and L.C.M of the following expressions:
(i) a2 + 2ab + b2
(ii) b2 – a2 + 2bc + c2
(iii) – b2+ a2 + 2ca + c2
Ans: An algebraic expression is a combination of constants, variables, and algebraic operations (+, -, ×, ÷). We can derive the algebraic expression for a given situation or condition by using these combinations.
Ans: The difference between polynomial and algebraic expressions is that polynomials include only variables and coefficients with mathematical operations (+, -, ×) but algebraic expressions include irrational numbers in the powers as well.
Moreover, polynomials are continuous function (e.g: x2 + 2x + 1) but algebraic expression may not be continuous sometimes (e.g: 1/(x2 – 1) is not continuous at 1).
Ans: Algebraic expression can be one of the following types:
(iv) Linear polynomial
(v) Quadratic polynomial
(vi) Cubic polynomial
Ans: Yes, any expression containing variables, numbers, and operation symbols is called an algebraic expression. So, 5x is an algebraic expression. It is also a monomial because it contains only one term.
Ans: The basic laws of algebra are the associative, commutative, and distributive laws. Check the following table to understand the laws.
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