# Algebraic Identities

• $(a+b)(a-b)=a^2-b^2$
• $(a+b)^2=a^2+2ab+b^2$
• $(a-b)^2=a^2-2ab+b^2$
• $(x+a)(x+b)=x^2+x(a+b)+ab$
• $(x+a)(x+b)(x+c)=x^3+x^2(a+b+c)+x(ab+bc+ca)+abc$
• $(a+b)^3=a^3+3ab(a+b)+b^3$
• $(a-b)^3=a^3-3ab(a-b)-b^3$
• $a^3+b^3=(a+b)(a^2-ab+b^2)$
• $a^3-b^3=(a-b)(a^2+ab+b^2)$
• $(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$
• $a^4+a^2b^2+b^4=(a^2+b^2+ab)(a^2+b^2-ab)$
• $(a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)$
• $(a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)-abc$

# Mensuration

## Area and Perimeter of Plane Figures

 Name Perimeter Area Triangle (a+b+c), where a, b, c are sides $\frac{1}{2}bh$ where "h" is the height from any vertex to the opposite side "b" Circle $2{\pi}r$ ${\pi}r^2$ Square $4a$ Where a is the side of a square $a^2$ Rectangle $2(l+b)$ Where l & b are the length & breadth $lb$ Trapezium $(a+b+c+d)$ Where a,b,c and d are the sides $\frac{1}{2}h(a+b)$ Where a and b are parallel sides of trapezium. And h is the perpendicular distance between two parallel sides. Parallelogram $2(a+b)$ Where a & b are the sides of Parallelogram $bh$ Where b is base and h is the perpendicular distance between base b and its parallel side. Rhombus $4a$ Where a is the side of a rhombus $\frac{1}{2}(d_{1}d_{2})$ Where d1 and d2 are diagonals of rhombus

## LSA(CSA) TSA & VOLUME of Solid Figures

 Name of the Solid LSA(CSA)in sq.units TSA in sq.units VOLUME in cubic units CUBE $4l^2$ Where lenght(l)=breadth(b)=height(h) $6l^2$ $l^3$ CUBOID $2h(l+b)$ $2(lb+bh+lh)$ $lbh$ PRISM 1)EQUILATERAL TRIANGLE RIGHT PRISM $Ph$ Where P=3a is the perimeter of base triangle $2B+Ph$ Where B= $\frac{\sqrt{3}a^2}{4}$ is the area of base $Bh$ Where B= $\frac{\sqrt{3}a^2}{4}$ 2)SQUARE BASED RIGHT PRISM $Ph$ Where P=4a is the perimeter of base square $2B+Ph$ Where B= $a^2$ is the area of base $Bh$ Where B= $a^2$ PYRAMID 1)EQUILATERAL TRIANGLE BASED RIGHT PYRAMID $\frac{1}{2}Pl$ Where P=3a is the perimeter of base triangle l is the slant height $B+\frac{1}{2}Pl$ Where B= $\frac{\sqrt{3}a^2}{4}$ is the area of base $\frac{1}{3}Bh$ Where B= $\frac{\sqrt{3}a^2}{4}$ 2)SQUARE BASED RIGHT PYRAMID $\frac{1}{2}Pl$ Where P=4a is the perimeter of base square l is the slant height $B+\frac{1}{2}Pl$ Where B= $a^2$ is the area of base $\frac{1}{3}Bh$ Where B= $a^2$ CYLINDER $2{\pi}rh$ Where r is the radius of circular base $2{\pi}r(r+h)$ where "h" is the height of cylinder ${\pi}r^2h$ CONE ${\pi}rl$ Where l is the slant height ${\pi}r(l+r)$ Where r is the radius of circular base $\frac{1}{3}{\pi}r^2h$ Where h is the height or depth of the cone FRUSTUM OF CONE ${\pi}(r_{1}+r_{2})l$ Where l= $\sqrt{h^2+(r_{1}-r_{2})^2}$ ${(r_{1}+r_{2})l+r_{1}^2+r_{2}^2}$ Where $r_{1}$ & $r_{2}$ are the radii of two bases $(r_{1}>r_{2})$ $\frac{1}{3}{\pi}h(r_{1}^2+r_{2}^2+r_{1}r_{2})$ Where h is the height or depth of the frustum ofcone SPHERE $4{\pi}r^2$ $4{\pi}r^2$ $\frac{4}{3}{\pi}r^3$ HEMISPHERE $2{\pi}r^2$ $3{\pi}r^2$ $\frac{2}{3}{\pi}r^3$