Algebra Formulas

1. \(a^{2}-b^{2}=(a+b)(a-b)\)
2. \((a+b)^{2}=a^{2}+2 a b+b^{2}\)
3. \(a^{2}+b^{2}=(a-b)^{2}+2 a b\)
4. \((a-b)^{2}=a^{2}-2 a b+b^{2}\)
5. \((a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 a c+2 b c\)
6. \((a-b-c)^{2}=a^{2}+b^{2}+c^{2}-2 a b-2 a c+2 b c\)
7. \((a+b)^{3}=a^{3}+3 a^{2} b+3 a b^{2}+b^{3} ;(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b)\)
8. \((a-b)^{3}=a^{3}-3 a^{2} b+3 a b^{2}-b^{3}\)
9. \(a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\)
10. \(a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)\)
11. \((a+b)^{4}=a^{4}+4 a^{3} b+6 a^{2} b^{2}+4 a b^{3}+b^{4}\)
12. \((a-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}\)
13. \(a^{4}-b^{4}=(a-b)(a+b)\left(a^{2}+b^{2}\right)\)
14. \(a^{5}-b^{5}=(a-b)\left(a^{4}+a^{3} b+a^{2} b^{2}+a b^{3}+b^{4}\right)\)
15. \((x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 x z\)
16. \((x+y-z)^{2}=x^{2}+y^{2}+z^{2}+2 x y-2 y z-2 x z\)
17. \((x-y+z)^{2}=x^{2}+y^{2}+z^{2}-2 x y-2 y z+2 x z\)
18. \((x-y-z)^{2}=x^{2}+y^{2}+z^{2}-2 x y+2 y z-2 x z\)
19. \(x^{3}+y^{3}+z^{3}-3 x y z=(x+y+z)\left(x^{2}+y^{2}+z^{2}-x y-y z-x z\right)\)
20. \(x^{2}+y^{2}=\frac{1}{2}\left[(x+y)^{2}+(x-y)^{2}\right]\)
21. \((x+a)(x+b)(x+c)=x^{3}+(a+b+c) x^{2}+(a b+b c+c a) x+a b c\)
22. \(x^{3}+y^{3}=(x+y)\left(x^{2}-x y+y^{2}\right)\)
23. \(x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)\)
24. \(x^{2}+y^{2}+z^{2}-x y-y z-z x=\frac{1}{2}\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right]\)
25. if n is a natural number, \(a^{n}-b^{n}=(a-b)\left(a^{n-1}+a^{n-2} b+\ldots+b^{n-2} a+b^{n-1}\right)\)
26. if n is even n = 2k, \(a^{n}+b^{n}=(a+b)\left(a^{n-1}-a^{n-2} b+\ldots+b^{n-2} a-b^{n-1}\right)\)
27. if n is odd n = 2k+1, \(a^{n}+b^{n}=(a+b)\left(a^{n-1}-a^{n-2} b+\ldots-b^{n-2} a+b^{n-1}\right)\)
28. \((a+b+c+\ldots)^{2}=a^{2}+b^{2}+c^{2}+\ldots+2(a b+b c+\ldots)\)
29. \(\begin{aligned}\left(a^{m}\right)\left(a^{n}\right)
&=a^{m+n} \\(a b)^{m} &=a^{m} b^{m} \\\left(a^{m}\right)^{n}
&=a^{m n} \end{aligned}\)
30. \(\begin{aligned} a^{0} &=1 \\ \frac{a^{m}}{a^{n}}
&=a^{m-n} \\ a^{m} &=\frac{1}{a^{-m}} \\ a^{-m}
&=\frac{1}{a^{m}} \end{aligned}\)

Root Maths Formulas

Square Root :

If x² = y then we say that square root of y is x and we write ?y = x

So, ?4 = 2, ?9 = 3, ?36 = 6
Cube Root:

The cube root of a given number x is the number whose cube is x.

we can say the cube root of x by ³?x

?xy = ?x * ?y
?x/y = ?x / ?y = ?x / ?y x ?y / ?y = ?xy / y.

Fractions Maths Formulas

What is fraction ?

Fraction is name of part of a whole.
Let the fraction number is 1 / 8.
Numerator : Number of parts that you of the top number(1)
Denominator : It is the number of equal part the whole is divided into the bottom number (8).
We hope the Maths Formulas for Class 6 to Class 12, help you. If you have any query regarding Class 6 to Class 12 Maths Formulas, drop a comment below and we will get back to you at the earliest.

FAQs on Maths Formulas

1. What is the best way to memorize Math Formulas?
The best way to remember math formulas to learn how to derive them.
If you can derive them then there is no need to remember them.
2. How to learn Mathematics Formulas?
Don’t try to learn the formula try learning the logic behind the formula and intuition behind it.
3. What is Math Formula?
Generally, each kind of maths has a formula or multiple formulas that help you work out a particular thing, whether it’s geometry, statistics, measurements, etc.
4. Is it necessary to know how does a math formula work?
It is indeed necessary to understand and be able to solve equations, either if you want to work as a mathematician, or any other field using mathematics, or if you want to be a math teacher or a teacher in a field that uses math.