All Algebra Formulas

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here have some important formula of algebra

Algebra is an important branch of mathematics. Here usually numbers of English alphabet a, b, x, y have to be calculated , Which we call variable. Many complex and large math can be solved very easily through this algebra . To do algebra we need to know some formulas .

QUESTION NO 1:-a+a=


formulas :-NO. 1     2a



QUESTION NO 2:-a+a+a=


formulas :-NO. 1     \(3\times a\)=3a



QUESTION NO 3:-a+a+a......... up to n=


formulas :-NO. 1     \(n\times a\)

QUESTION NO 4:-\(a\times a\)=


formulas :-NO. 1    \(a^{1+1}\) =\(a^{2}\)



QUESTION NO 5:-\(a\times a \times a \)=


formulas :-NO. 1    \(a^{1+1+1}\)= \(a^{3}\)

QUESTION NO 6:-\(a\times a \times a \)................... up to n =


formulas :-NO. 1     \(a^{n}\)

QUESTION NO 7:-\(a^{m}\times a^{n}\)=


formulas :-NO. 1     \(a^{m+n}\)

QUESTION NO 8:-\(a^{m}\div a^{n}\)=


formulas :-NO. 1     \(a^{m-n}\)

QUESTION NO 9:-\((a^{m})^{n}\)=


formulas :-NO. 1     \(a^{m\times n}\)

QUESTION NO 10:-\((ab)^{m}\)=


formulas :-NO. 1     \(a^{m}\times b^{m}\)

QUESTION NO 11:-\((\frac{a}{b})^{m}\)=


formulas :-NO. 1     \(\frac{a^{m}}{b^{m}}\)

QUESTION NO 12:-\((abc)^{m}\)=


formulas :-NO. 1     \(a^{m}\times b^{m}\times c^{m}\)

QUESTION NO 13:-\((a)^{0}\)=


formulas :-NO. 1     1 \(a\neq 0\)

QUESTION NO 14:-\(a^{m}\)=


formulas :-NO. 1     \(\frac{1}{a^{-m}}\)

QUESTION NO 15:-\(a^{-m}\)=


formulas :-NO. 1     \(\frac{1}{a^{m}}\)

QUESTION NO 16:-\(\sqrt[n]{a}\)=


formulas :-NO. 1    \(a^{\frac{1}{n}}\)

QUESTION NO 17:-\(\sqrt[n]{a^{m}}\)=


formulas :-NO. 1    \(a^{\frac{m}{n}}\)

QUESTION NO 18:-if is \(a^{m}=b^{m}\)


formulas :-NO. 1     then will be a=b

QUESTION NO 19:-if is \(a^{m}=a^{n}\)


formulas :-NO. 1     then will be m=n

QUESTION NO 20:-\((a+b)^{2}\)=


formulas :-NO. 1     \(a^{2}+2ab+b^{2}\)

formulas :-NO. 2     \((a-b)^{2}\)+4ab

QUESTION NO 21:-\(a^{2}+b^{2}=\)


formulas :-NO. 1    \((a+b)^{2}\)-2ab

formulas :-NO. 2    \((a-b)^{2}\)+2ab

QUESTION NO 22:-\((a+b+c)^{2}\)=


formulas :-NO. 1    \(a^{2}+b^{2}+c^{2}+2(ab+bc+ca)\)

QUESTION NO 23:-\(a^{2}+b^{2}+c^{2}\)=


formulas :-NO. 1    \((a+b+c)^{2}-2(ab+bc+ca)\)

QUESTION NO 24:-\((a-b)^{2}\)=


formulas :-NO. 1    \(a^{2}-2ab+b^{2}\)

formulas :-NO. 2    \((a+b)^{2}\)-4ab

QUESTION NO 25:-\(a^{2}-b^{2}=\)


formulas :-NO. 1    (a+b)(a-b)

QUESTION NO 26:-\((a+b)^{2}+(a-b)^{2}=\)


formulas :-NO. 1     \(2(a^{2}+b^{2})=\)

QUESTION NO 27:-\((a+b)^{2}-(a-b)^{2}=\)


formulas :-NO. 1    4ab

QUESTION NO 28:-2(ab+bc+ca)=


formulas :-NO. 1    \((a+b+c)^{2}-(a^{2}+b^{2}+c^{2})=\)

QUESTION NO 29:-ab=


formulas :-NO. 1    \((\frac{a+b}{2})^{2}-(\frac{a-b}{2})^{2}\)

QUESTION NO 30:-4ab=


formulas :-NO. 1     \((a+b)^{2}-(a-b)^{2}\)

QUESTION NO 31:-\((a+b)^{3}\)=


formulas :-NO. 1    \(a^{3}+3a^{2}b+3ab^{2}+b^{3}\)

formulas :-NO. 2    \(a^{3}+b^{3}+3ab(a+b)\)

QUESTION NO 32:-\((a-b)^{3}\)=


formulas :-NO. 1    \(a^{3}-3a^{2}b+3ab^{2}-b^{3}\)

formulas :-NO. 2    \(a^{3}-b^{3}-3ab(a-b)\)

QUESTION NO 33:-\(a^{3}+b^{3}\)=


formulas :-NO. 1    \((a+b)^{3}-3ab(a+b)\)

formulas :-NO. 2    \((a+b)(a^{2}-ab+b^{2})\)

QUESTION NO 34:-\(a^{3}-b^{3}\)=


formulas :-NO. 1    \((a-b)^{3}+3ab(a-b)\)

formulas :-NO. 2    \((a-b)(a^{2}+ab+b^{2})\)

QUESTION NO 35:-\((a+b+c)^{3}\)=


formulas :-NO. 1    \(a^{3}+b^{3}+c^{3}+3(a+b)(b+c)(c+a)\)

QUESTION NO 36:-\((a+b+c)^{3}\)=


formulas :-NO. 1    \(a^{3}+b^{3}+c^{3}+3(a+b)(b+c)(c+a)\)


Some examples of addition of two variables.

Example 1:- 5a+7a= Ans:-12a ,

Example 2:- 3a+5a= Ans:-8a ,

Example 3:- 2a+5a= Ans:-7a ,


Example 4:- 2a+5b= Ans:-2a+5b , If this is the case, it cannot be added . Because the values of variable-a and variable-b are not the same . \(a\neq b\)

Example 5:- \(a + a^{2}\) , If this is the case, it cannot be added . Because the values of variable-a and variable-\(a^{2}\) are not the same . \(a\neq a^{2}\) .

Some examples of addition of three variables.

Example 1:- 5a+7a+2a= Ans:-14a ,

Example 2:- 3a+5a+a= Ans:-9a ,

Example 3:- 2a+5a+10a= Ans:-17a ,


Example 4:- 2a+3a+2b= Ans:-5a+2b , If this is the case, it cannot be added . Because the values of a and b are not the same . \(a\neq b\)

Example 5:- 2a+3b+2c= Ans:-2a+3b+2c , If this is the case, it cannot be added . Because the values of a and b are not the same . \(a\neq b\) or \(a\neq c\) or \(b\neq c\)

Some examples of multiplication of variables

Example 1:- \(a^{2}\times a^{5}\)=\(a^{2+5}\) =\(a^{7}\) , Powers must be added while multiplying .

Example 2:- \(a^{1}\times a^{7}\)=\(a^{1+7}\) =\(a^{8}\)

If the variables are equal during multiplication, then the powers of the variables have to be added (Sum).


Example 3:- \(7a^{1}\times 3a^{7}\)=\(7 \times 3 \times a^{1+7}\) =\(21a^{8}\) ,