Algebra is a branch of mathematics that substitutes letters for numbers. An algebraic equation depicts a scale, what is done on one side of the scale with a number is also done to either side of the scale. The numbers are constants. Algebra also includes real numbers, complex numbers, matrices, vectors and much more. X, Y, A, B are the most commonly used letters that represent algebraic problems and equations.
Algebra Formulas from Class 8 to Class 12  Algebra Formulas For Class 8  Algebra Formulas For Class 9  Algebra Formulas For Class 10  Algebra Formulas For Class 11  Algebra Formulas For Class 12 

Important Formulas in Algebra
Here is a list of Algebraic formulas –
 a^{2} – b^{2} = (a – b)(a + b)
 (a + b)^{2} = a^{2} + 2ab + b^{2}
 a^{2} + b^{2} = (a + b)^{2} – 2ab
 (a – b)^{2} = a^{2} – 2ab + b^{2}
 (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca
 (a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2ab + 2bc – 2ca
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} ; (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3 }= a^{3} – b^{3} – 3ab(a – b)
 a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})
 a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})
 (a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4}
 (a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4}
 a^{4} – b^{4} = (a – b)(a + b)(a^{2} + b^{2})
 a^{5} – b^{5} = (a – b)(a^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4})
 If n is a natural number a^{n} – b^{n} = (a – b)(a^{n1} + a^{n2}b+…+ b^{n2}a + b^{n1})
 If n is even (n = 2k), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +…+ b^{n2}a – b^{n1})
 If n is odd (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +a^{n3}b^{2}… b^{n2}a + b^{n1})
 (a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + ….)
 Laws of Exponents (a^{m})(a^{n}) = a^{m+n} ; (ab)^{m} = a^{m}b^{m }; (a^{m})^{n} = a^{mn}
 Fractional Exponents a^{0} = 1 ; \(\begin{array}{l}\frac{a^{m}}{a^{n}} = a^{mn}\end{array} \);\(\begin{array}{l}a^{m}\end{array} \)=\(\begin{array}{l}\frac{1}{a^{m}}\end{array} \);\(\begin{array}{l}a^{m}\end{array} \)=\(\begin{array}{l}\frac{1}{a^{m}}\end{array} \)
 Roots of Quadratic Equation

 For a quadratic equation ax^{2} + bx + c = 0 where a ≠ 0, the roots will be given by the equation as \(\begin{array}{l}x=\frac{b\pm \sqrt{b^{2}4ac}}{2a}\end{array} \)
 Δ = b^{2} − 4ac is called the discriminant
 For real and distinct roots, Δ > 0
 For real and coincident roots, Δ = 0
 For nonreal roots, Δ < 0
 If α and β are the two roots of the equation ax^{2} + bx + c = 0 then, α + β = (b / a) and α × β = (c / a).
 If the roots of a quadratic equation are α and β, the equation will be (x − α)(x − β) = 0
 For a quadratic equation ax^{2} + bx + c = 0 where a ≠ 0, the roots will be given by the equation as
 Factorials

 n! = (1).(2).(3)…..(n − 1).n
 n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
 0! = 1
 \(\begin{array}{l}(a + b)^{n} = a^{n}+na^{n1}b+\frac{n(n1)}{2!}a^{n2}b^{2}+\frac{n(n1)(n2)}{3!}a^{n3}b^{3}+….+b^{n}, where\;,n>1\end{array} \)
Read more:
Solved Examples
Example 1: Find out the value of 5^{2} – 3^{2
}Solution:
Using the formula a^{2} – b^{2} = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2
= 16
Example 2: 4^{3}
Solution:
Using the exponential formula (a^{m})(a^{n}) = a^{m+n }where a = 4
4^{3}
Using the formula a^{2} – b^{2} = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2
\(\begin{array}{l}\times\end{array} \)
8= 16
Example 2: 4^{3}
\(\begin{array}{l}\times\end{array} \)
4^{2} = ?Solution:
Using the exponential formula (a^{m})(a^{n}) = a^{m+n }where a = 4
4^{3}
\(\begin{array}{l}\times\end{array} \)
4^{2
}= 4^{3+2
}= 4^{5
}= 1024
Thank you as you prepering us these important maths
thanks for this information
Good
Thanks for the information
Useful for every student
Its good
Very brilliant application for study
You just done it like a godgift to me. I needed it . Thankgod
Very much thanks it is very very helpful for me .
It helps me to complete my homework of school..
Thanku soooooo mmmuuuccchhhh…
all at a place!!!!good for revision before competitive exams.
Thanks for the quality content
Nice
Nice aap byjus 👍😍♥️
Thanks for helping me with the formula
I like BYJU’S it tells me the math formulas.
Your service is nice
😇
Excellent app
Every one would like to learn this!!!
Very usefull.
wow its amazing and useful
This is good learning for good app
very helpfull I really recomend you
thank you Byjus
Thank you for these formulas it may help all the people while solving problems
Its good
It’s really good👍👍👍
Useful formulae
that was very useful
thank U
Good piece of information thanks. BYJU S
Thank u for posting this usefulformula to slove the problem
It’s really good
Really useful, I would love to ask more questions on this platform if required.
You are best byjus these formulas are very helpful for me thank you 🤩🤩
THANKS . I LOVE YOUR SERVICE FOR EDUCATION
WOW this is a great site love this byjus
Amazing it helped me a lot .
The one of the best (lerning app)🖥️🖥️⌨️ in the world 🌎🌎🌍📔📕📓📚📖🗞️
Thank you so much