Algebra Identities Practice Guide
Square Identities:-
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
Example: (x + 5)2 = x2 + 2(x)(5) + 52 = x2 + 10x + 25
(x – 5)2 = x2 – 2(x)(5) + 52 = x2 – 10x + 25
Product Identity:-
a2 - b2 = (a + b) (a – b)
Example: 82 – y2 = (8 + y) (8 – y)
Cube Identities:-
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 – 3a2b + 3ab2 – b3
a3 + b3 = (a + b) (a2 – ab + b2)
a3 – b3 = (a – b) (a2 + ab + b2)
Example: (x + 2)3 = x3 + 3(x)2(2) + 3(x)(2)2 + 23 = x3 + 6x2 + 12x + 8
(x – 2)3 = x3 – 3(x)2(2) + 3(x)(2)2 – 23 = x3 – 6x2 + 12x – 8
x3 + 27 = x3 + 33 = (x + 3) (x2 – (x)3 + 33)
x3 – 27 = x3 – 33 = (x – 3) (x2 + (x)3 + 33)
Created by Ash
Algebra Practice Notes
Square Identities:-
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
Example: (x + 5)2 = x2 + 2(x)(5) + 52 = x2 + 10x + 25
(x – 5)2 = x2 – 2(x)(5) + 52 = x2 – 10x + 25
Product Identity:-
a2 - b2 = (a + b) (a – b)
Example: 82 – y2 = (8 + y) (8 – y)
Cube Identities:-
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 – 3a2b + 3ab2 – b3
a3 + b3 = (a + b) (a2 – ab + b2)
a3 – b3 = (a – b) (a2 + ab + b2)
Example: (x + 2)3 = x3 + 3(x)2(2) + 3(x)(2)2 + 23 = x3 + 6x2 + 12x + 8
(x – 2)3 = x3 – 3(x)2(2) + 3(x)(2)2 – 23 = x3 – 6x2 + 12x – 8
x3 + 27 = x3 + 33 = (x + 3) (x2 – (x)3 + 33)
x3 – 27 = x3 – 33 = (x – 3) (x2 + (x)3 + 33)
Created by Ash
Algebra Practice Notes
