# Algebraic Identities

## Concept Lectures

Session # 1 : This session covers basic Algebraic Identities related to binomials and trinomials - Part I

Session # 2 : This session covers basic Algebraic Identities related to binomials and trinomials - Part II. Some example problems on expansion using identities have also been solved.

## Problem Solving Sessions

Session # 3 : Solved Examples : Using Algebraic Identities evaluate a) 103 x 97 and b) (0.99)^2

Session # 4 : Solved Examples : 1. Simplify : (2x+5y+3)(2x+5y+4) 2. If x + 1/x = 6, Find the value of x^2+1/x^2 and x^4+1/x^4

Session # 5 : Solved Examples : If x^2 + 1/x^2 = 27, then find the value of a) x + 1/x, b) x - 1/x

Session # 6 : 1. Prove that 2a^2 +2b^2+ 2c^2 - 2ab - 2bc - 2ca = (a-b)^2 + (b-c)^2 + (c-a)^2 2. Find the coefficient of x^2 in the expansion of (x^2+x+1)^2 + (x^2-x+1)^2

## Concept Lectures

Session # 7 : Square of Trinomials

## Problem Solving Sessions

Session # 8 : Problems related to expansion of square of trinomials

Session # 9 : If a+b+c = 9 and ab + bc + ca = 40, find the value of a^2 + b^2 + c^2

## Concept Lectures

Session # 10 : Cubes of Binomials (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

## Problem Solving Sessions

Session # 11 : Solved Example: 1) Expand (2x + 3y)^3 (2) Expand (1/3x - 2/5y)^3

Session # 12 : Solved Example: If (x^2 + 1/x^2) =83. Find the value of (x^3 - 1/x^3)

Session # 13 : Solved Example: Q1 : If (x - y) = 4 and xy = 21 then find the value of x^3 - y^3; Q2. If x + 1/x = 7, find the value of x^3 + 1/x^3

Session # 14 : Solved Example: Q: Simplify : ( 4x + 2y )^3 - (4x - 2y )^3

Session # 15 : Solved Example: Sum and Difference of Cubes Q: Find the product (7a-5b)(49a^2 + 35ab + 25b^2)

Session # 16 : Solved Example: Sum and Difference of Cubes Q: Find the product: (0.9x + 0.7y)(0.81x^2 - 0.63xy + 0.49y^2)

Session # 17 : Solved Example: Sum and Difference of Cubes Q: Simplify: (6m-n)(36m^2 + 6mn + n^2) - (3m + 2n)^3

Session # 18 : Solved Example: Sum and Difference of Cubes Q: If a + b = 7 and ab =12 then find the value of (a) a^3 + b^3 (b) a^2 - ab + b^2

## Concept Lectures

Session # 19 : Special Identity: a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca); CONDITIONAL IDENTITY: If a + b + c = 0; then a^3 + b^3 + c^3 = 3abc

## Problem Solving Sessions

Session # 20 : Q: Find the product: (x - y + 2z)(x^2 +y^2 + 4z^2 - xy -2yz + 2zx)

Session # 21 : Q: If a + b + c = 6 and ab + bc + ca = 11 then find the value of a^3 + b^3 + c^3 - 3abc

Session # 22 : Q: Simplify: [(a^2 - b^2)^2 + (b^2 - c^2)^2 + (c^2 - a^2)^2]/[(a - b) + (b - c) + (c - a)]

## Concept Lectures

Session # 23 : Sophie Germain Identity