all identities portfolio^

(i) (a + b)2 = a2 + 2ab + b2

(ii) (a– b)2 = a2– 2ab + b2

(iii) a2– b2 = (a + b) (a – b)

(iv) a3 + b3 = (a + b) (a2– ab + b2)

(v) a3– b3 = (a – b) (a2 + ab + b2)

(vi) (a + b)3 = a3 + b3 + 3ab (a + b)

(vii) (a– b)3 = a3– b3– 3ab (a – b)

(viii) a3 + b3 + c3– 3abc = (a + b + c) (a2 + b2 + c2– ab – bc – ac)

• surface and volume formulas

• 3d shapes

Cube

• Surface Area: 6L² where L is the dimension of its side.

• Volume: L3 where L is the dimension of its side.

Cuboid

• Surface Area: 2(LB+ BH+ LH).

• Lateral Surface Area: 2(L + B) H (where L= Length, B= Breadth and H= Height)

• Volume: LBH

Right Circular Cylinder

• Lateral Surface Area: 2
• πRH
• πRH.
• Total Surface Area:  
• 2πR(H+R)
• 2πR(H+R) 
• Volume:
• πR
• 2
• H
• πR2H (where R= Radius, H= Height).

Right Circular Cone

• Lateral Surface Area:
• πRL
• πRL
• Total Surface Area:
• ρπR(L+R)
• ρπR(L+R)
• Volume:
• 2
• 3
• 
  
• πR
• 2
• H
• 23πR2H (where R= Radius, L=Slant Height and H= Height)

Sphere

• Surface Area:
• 4πR
• 2
• 4πR2
• Volume: 
• 4
• 3
• 
  
• πR
• 3
• 43πR3(where R= Radius)

Hemisphere

• Curved Surface Area:
• 2πR
• 2
• 2πR2
• Total Surface Area:
• 3πR
• 2
• 3πR2
• Volume:
• 
  
• 2
• 3
• 
  
• πR
• 3
• 23πR3 (where R= Radius).

square root sprial