# List of Algebra Formulas

Algebra is an integral part of Mathematics. It uses symbols and letters to represent quantities and numbers in equations and formulae. The two basic types of algebra are Elementary algebra and Modern algebra. To study algebra students need to have a clear understanding of various formulas, terms and concepts. Learning these formulas and applying them can help them attain a better score in mathematics.

We believe that having access to the list of algebra formulas for class 10 all in a single page can be really beneficial for the students. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas. ## Algebraic Identities For Class 10

(a+b)2$\mathbf{(a+b)^{2}}$ =a2+2ab+b2$=a^2+2ab+b^{2}$
(ab)2$\mathbf{(a-b)^{2}}$ =a22ab+b2$=a^{2}-2ab+b^{2}$
(a+b)(ab)$\mathbf{\left (a + b \right ) \left (a – b \right ) }$ =a2b2$= a^{2} – b^{2}$
(x+a)(x+b)$\mathbf{ \left (x + a \right )\left (x + b \right ) }$ =x2+(a+b)x+ab$= x^{2} + \left (a + b \right )x + ab$
(x+a)(xb)$\mathbf{\left (x + a \right )\left (x – b \right ) }$ =x2+(ab)xab$= x^{2} + \left (a – b \right )x – ab$
(xa)(x+b)$\mathbf{\left (x – a \right )\left (x + b \right )}$ =x2+(ba)xab$= x^{2} + \left (b – a \right )x – ab$
(xa)(xb)$\mathbf{\left (x – a \right )\left (x – b \right ) }$ =x2(a+b)x+ab$= x^{2} – \left (a + b \right )x + ab$
(a+b)3$\mathbf{\left (a + b \right )^{3}}$ =a3+b3+3ab(a+b)$= a^{3} + b^{3} + 3ab\left (a + b \right )$
(ab)3$\mathbf{\left (a – b \right )^{3} }$ =a3b33ab(ab)$= a^{3} – b^{3} – 3ab\left (a – b \right )$
(x+y+z)2$\mathbf{(x + y + z)^{2}}$ =x2+y2+z2+2xy+2yz+2xz$= x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz$
(x+yz)2$\mathbf{(x + y – z)^{2}}$ =x2+y2+z2+2xy2yz2xz$= x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz$
(xy+z)2$\mathbf{(x – y + z)^{2} }$ =x2+y2+z22xy2yz+2xz$= x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz$
(xyz)2$\mathbf{(x – y – z)^{2}}$ =x2+y2+z22xy+2yz2xz$= x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz$
x3+y3+z33xyz$\mathbf{x^{3} + y^{3} + z^{3} – 3xyz }$ =(x+y+z)(x2+y2+z2xyyzxz)$= (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz -xz)$
x2+y2$\mathbf{x^{2} + y^{2}}$ =12[(x+y)2+(xy)2]$= \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]$
(x+a)(x+b)(x+c)$\mathbf{(x + a) (x + b) (x + c) }$ =x3+(a+b+c)x2+(ab+bc+ca)x+abc$= x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc$
x3+y3$\mathbf{x^{3} + y^{3}}$ =(x+y)(x2xy+y2)$= (x + y) (x^{2} – xy + y^{2})$
x3y3$\mathbf{x^{3} – y^{3}}$ =(xy)(x2+xy+y2)$= (x – y) (x^{2} + xy + y^{2})$
x2+y2+z2xyyzzx$\mathbf{x^{2} + y^{2} + z^{2} -xy – yz – zx }$ =12[(xy)2+(yz)2+(zx)2]$= \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]$

## Linear Equation in Two Variables

a1x+b1y+c1$\mathbf{a_{1}x + b_{1}y + c_{1} }$ =0$= 0$
a2x+b2y+c2$\mathbf{a_{2}x+ b_{2}y + c_{2}}$ =0$= 0$

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# List of geometry formulas for Class 10

Geometry is an important part of Mathematics. There are various formulas to calculate area, base area, lateral area, surface area and perimeter for various geometric shapes. To study geometry, students need to have a clear understanding of various theorems, formulas and properties. Learning these formulas and applying them can help them attain a better score in mathematics.

We believe that having access to the list of geometry formulas for class 10 all in a single page can be really beneficial for you. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas. Geometry Formulas for Class 10 Name Formula Area of Triangle Area=12base⋅height$Area = \frac{1}{2} base \cdot height$ Pythagorean Theorem a2+b2=c2$a^{2} + b^{2} = c^{2}$ Area of a Circle Area=πr2$Area = \pi r^{2}$ Circumference of a Circle C=2πr$C = 2\pi r$ or πd$\pi d$ Area of a Parallelogram Area=base⋅height$Area = base \cdot height$ Area of a Trapezoid Area=base1+base22⋅height$Area =\frac{base_{1}+base_{2}}{2}\cdot height$ Area of a Kite or a Rhombus Area=12diagonal1⋅diagonal2$Area = \frac{1}{2} diagonal_{1}\cdot diagonal_{2}$ Area of a Square Area=side2$Area = side^{2}$ Area of a Regular Polygon Area=12perimeter⋅apothem$Area = \frac{1}{2}perimeter\cdot apothem$ Number of Diagonal in n-sided Polygon Diagonals=n(n−3)2$Diagonals = \frac{n \left (n-3 \right )}{2}$ Slope m=y2−y1x2−x1=riserun$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}$ Midpoint Formula (xmp,ymp)=(x1+x22),(y1+y22)$\left ( x_{mp},y_{mp} \right )=\left ( \frac{x_{1}+x_{2}}{2} \right ),\left ( \frac{y_{1}+y_{2}}{2} \right )$ Distance Formula d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√$d=\sqrt{\left ( x_{2}-x_{1} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}}$ Equation of a Circle (x−h)2+(y−k)2=r2$\left ( x-h \right )^{2}+\left ( y-k \right )^{2}=r^{2}$

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# Coordinate geometry for class 10

Coordinate geometry is that part of mathematics which provides a connection between algebra and geometry through graphs of lines and curves. There are certain formulas related to coordinate geometry. These formulas are used to find the distance between the two points whose coordinates are given and the area of the triangle formed by three given points. You can also use these formulas to find the coordinates of the point which divides a line segment joining two given points in a given ratio. Learning these formulas and applying them can help students attain a better score in mathematics.

We believe that having access to the list of formulas for coordinate geometry for class 10 on a single page can be really beneficial for students. Therefore, we have compiled this list and presented it to you through this website. Check this out and download the formulas for further reference. Also, make sure to navigate to the other formulas. ## 1. Distance formula

Distance between the points AB is given by D= √(x1-x2)²+(y2-y1)²

Distance of Point A from origin D = √x²+y²

## 2. Section formula

A point P(x,y) which divides the line segment AB in the ratio m1 and m2 is given by x=m1x2+m2x1⁄m1+m2 y=m1y2+m2y1⁄m1+m2

The midpoint P is given by (x1+x2/2), (y1+y2/2)

## 3. Area of triangle

Area of triangle ABC of coordinates A(x1,y1), B(x2,y2) and C(x3,y3)

A=½[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

For points A, B and C to be collinear, the value of A should be zero.

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