# Algebra Formulas For Class 9

Algebra is a part of Mathematics in which general symbols and letters are used to represent quantities and numbers in equations and formulae. There are two parts in algebra - Elementary algebra and Modern algebra (Abstract algebra). Algebra formulas for class 9 include formulas related to algebra identities or expressions.

Algebra Identities chapter is introduced in class 9. This is a little tricky chapter where one needs to learn all the formula and apply them accordingly.

 Algebraic Identities For Class 9 $(a+b)^{2}=a^2+2ab+b^{2}$ $(a-b)^{2}=a^{2}-2ab+b^{2}$ $\left (a + b \right ) \left (a – b \right ) = a^{2} – b^{2}$ $\left (x + a \right )\left (x + b \right ) = x^{2} + \left (a + b \right )x + ab$ $\left (x + a \right )\left (x – b \right ) = x^{2} + \left (a – b \right )x – ab$ $\left (x – a \right )\left (x + b \right ) = x^{2} + \left (b – a \right )x – ab$ $\left (x – a \right )\left (x – b \right ) = x^{2} – \left (a + b \right )x + ab$ $\left (a + b \right )^{3} = a^{3} + b^{3} + 3ab\left (a + b \right )$ $\left (a – b \right )^{3} = a^{3} – b^{3} – 3ab\left (a – b \right )$ $(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz$ $(x + y – z)^{2} = x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz$ $(x – y + z)^{2} = x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz$ $(x – y – z)^{2} = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz$ $x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz -xz$ $x^{2} + y^{2} = \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]$ $(x + a) (x + b) (x + c) = x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc$ $x^{3} + y^{3} = (x + y) (x^{2} – xy + y^{2})$ $x^{3} – y^{3} = (x – y) (x^{2} + xy + y^{2})$ $x^{2} + y^{2} + z^{2} -xy – yz – zx = \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]$