# Algebraic Formulas for Class 9:

Algebra covers a major portion of mathematics and mainly deals with calculation and solution based measures. It is defined as generalization of arithmetic in which letters representing numbers are combined accordingly by the rule of arithmetic. It also deals with the properties of abstract entities such as complex numbers, matrices, vectors, sets, groups, rings etc. converted in symbolic form in terms of arithmetic.

It is different from arithmetic as algebra uses symbols and letters which stands for numbers whereas arithmetic has only the use of the number. Algebra gives all the possible methods for writing formulas and solving equations that are much clearer and easier than the writing everything in words as done earlier.

It’s a separate chapter in class 9th named as algebraic identities. In this chapter, you will read about all the basic components of algebra serially. Before going through this chapter you must revise all the formulas which you learn in class 8. It will make you easy dealing with this chapter. This chapter is so important because it will be needed every time either you are studying science, mathematics or commerce in higher sections. so learn every formula to score better marks in this section.

## We have arranged all the formulas which you will need in solving algebra related problems in class 9th.

 Algebraic Formulas For Class 9th (a+b)2 = a2+2ab+b2 (a−b)2 = a2−2ab+b2 (a+b)(a–b) = a2–b2 (x+a)(x+b) = x2+(a+b)x+ab (x+a)(x–b) = x2+(a–b)x–ab (x–a)(x+b) = x2+(b–a)x–ab (x–a)(x–b) = x2–(a+b)x+ab (a+b)3=a3+b3+3ab(a+b) (a–b)3 = a3–b3–3ab(a–b) (x+y+z)2 = x2+y2+z2+2xy+2yz+2xz (x+y–z)2 = x2+y2+z2+2xy–2yz–2xz (x–y+z)2 = x2+y2+z2–2xy–2yz+2xz (x–y–z)2 = x2+y2+z2–2xy+2yz–2xz
 x3+y3+z3–3xyz = (x+y+z)(x2+y2+z2–xy–yz−xz) $${x^{2}+y^{2}=\frac{1}{2}[{(x+y)}^{2}+(x–y)^{2}]}$$ (x+a)(x+b)(x+c) = x3+(a+b+c)x2+(ab+bc+ca)x+abc x3+y3 = (x+y)(x2–xy+y2) X3–y3 = (x–y)(x2+xy+y2) $${x^{2}+y^{2}+z^{2}−xy–yz–zx=\frac{1}{2}{[(x−y)^2+(y−z)^{2}+(z−x)^{2}]}}$$

Learn it wisely.