Arithmetic
Additive Identity
Arithmetic Progression
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Distributivity of Multiplication over Addition
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method
Algebra
Cartesian System
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose
Geometry
Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Quadrilateral
Trigonometry
Trigonometry Ratios
Data-Handling
Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range

Videos
Solved Problems
Home >> Standard Identities & their applications >> (x + a) (x + b) = x2 + x(a + b) + ab >>

(X + A) (X + B)

(a + b)2 = a2 + b2 + 2ab (a - b)2 = a2 + b2 - 2ab a2 - b2 = (a + b) (a - b) (x + a) (x + b) = x2 + x(a + b) + ab (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a + b)3 = a3 + b3 + 3ab(a + b) (a - b)3 = a3 - b3 - 3ab(a - b) a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

Before you understand (x + a) (x + b) = x2 + x(a + b) + ab, you are advised to read:

How to Multiply Variables ?
How to Multiply Polynomials ?
What is Exponential Form ?

How this identity of (x + a) (x + b) = x2 + x(a + b) + ab is obtained

Taking LHS of the identity:
(x + a) (x + b)

Multiply as we do multiplication of two binomials and we get:
= x(x + b) + a(x + b)
= x2 + bx + ax + ab

Since, bring out x as common from bx and ax & we get:
= x2 + x(b + a) + ab

Hence, in this way we obtain the identity i.e. (x + a) (x + b) = x2 + x(a + b) + ab

Following are few applications of identity third:


Example 1: Solve (p + 10) (p + 5)
Solution: This proceeds as:
Given polynomial (p + 10) (p + 5) represents identity third i.e. (x + a) (x + b)
Where x = p, a = 10 and b = 5

Now apply values of x, a and b on the identity i.e. (x + a) (x + b) = x2 + x(a + b) + ab and we get:
(p + 10) (p + 5) = (p)2 + p(10 + 5) + (10 X 5)
= p2 + p(15) + 50
= p2 + 15p + 50

Hence, (p + 10) (p + 5) = p2 + 15p + 50



Example 2: Solve (5c2 + 3) (5c2 + 2)
Solution: This proceeds as:
Given polynomial (5c2 + 3) (5c2 + 2) represents identity third i.e. (x + a) (x + b)
Where x = 5c2, a = 3 and b = 2

Now apply values of x, a and b on the identity i.e. (x + a) (x + b) = x2 + x(a + b) + ab and we get:
(5c2 + 3) (5c2 + 2) = (5c2)2 + 5c2 (3 + 2) + (3 X 2)

= 5c4 + 5c2(5) + 6
= 5c4 + 25c2 + 6

Hence, (5c2 + 3) (5c2 + 2) = 5c4 + 25c2 + 6

Copyright@2022 Algebraden.com (Math, Algebra & Geometry tutorials for school and home education)