**IMPORTANT FORMULAS IN ALGEBRA**

SOME IMPORTANT ALGEBRAICAL FORMULA & IDENTITIES used in algebra you must know with their derivation. These maths formulas are used not only in algebra but in every sphere of mathematics. These algebraic expressions make the maths problem easy. Here is some important algebraical formula with their derivation. These are the some basic formula you must understand deeply with their application in solving different types of problems. Here, you will learn **some important algebraical formula** with their derivation.

1. (a+b)^{2}= (a+b)(a+b) (Multiply It)

=a^{2} +ab + ab+b^{2}

=a^{2} +2ab+b^{2}

=a^{2} + 2ab + b^{2}

(a+b)^{2} =a^{2} + 2ab + b^{2}

2. (a-b)^{2}= (a-b)(a-b) (Multiply It)

=a^{2} – ab – ab + b^{2}

=a^{2} – 2ab + b^{2}

a^{2} – 2ab + b^{2}

(a-b)^{2} = a^{2} – 2ab + b^{2}

3. (a+b)(a-b) =(a+b)(a-b) {Multiply it)

=a^{2} – ab + ab – b^{2}

=a^{2} – b^{2}

a^{2} – b^{2}

(a+b)(a-b) = a^{2} – b^{2}

4. (a+b+c)^{2} = (a+b+c)(a+b+c)

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

=a^{2} +b^{2} +c^{2} + 2ab + 2bc + 2ac

{If anyone is negative in a,b,c then put a= -a, b=-b & c=-c in above formula according to question

(a+b+c)^{2} =a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ac

5. (a+b)^{3}=(a+b)^{2} (a+b)

=(a^{2} + 2ab +b^{2})(a+b)

=(a)^{3} + a^{2}b + 2a^{2}b + 2ab^{2} + ab^{2} +(b)^{3}

=(a)^{3} + 3a^{2}b + 3b^{2}a + (b)^{3}

= (a)^{3}+3ab(a+b)+(b)^{3}

(a+b)^{3}= (a)^{3}+3ab(a+b)+(b)^{3}

6. (a-b)^{3}=(a-b)^{2} (a-b)

=(a^{2} -2ab +b^{2})(a-b)

=(a)^{3}-a^{2}b – 2a^{2}b + 2ab^{2} +a^{2} + (b)^{3}

=(a)^{3}-3a^{2}b+3b^{2}a-(b)^{3}

= (a)^{3}-3ab(a-b)-(b)^{3}

(a-b)^{3} =(a)^{3}-3ab(a-b)-(b)^{3}

7. (a)^{3}+(b)^{3}=(a+b)^{3}-3ab(a+b)

=(a+b)((a+b)^{2}-3ab))

=(a+b)(a^{2} + 2ab +b^{2} -3ab)

=(a+b)(a^{2} – ab + b^{2})

(a)^{3} + (b)^{3} = (a+b)(a^{2} – ab + b^{2})

8. (a)^{2}-(b)^{3}=(a-b)^{3}+3ab(a-b)

=(a-b)( (a-b)^{2} + 3ab )

=(a-b)(a^{2} – 2ab + b^{2} + 3ab)

=(a-b)(a^{2} + ab + b^{2})

(a)^{3} -(b)^{3} =(a-b)(a^{2} +ab + b^{2})