Algebraic Identities
Contents
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)
