| 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 >> Polynomials >> Multiplication of Polynomials >> Multiplication of Binomial & Trinomial >> Multiplication of Binomial & Trinomial
Before you understand this concept, you are advised to read:
What are Monomials & Binomials ?
What are Terms of Polynomial ?
While multiplying a binomial and a trinomial you will find following situations:
Multiply Binomial and Trinomial
Example 1: Multiply (5a + b) and (a + b + c)
Example 2: Multiply (3p - 2) and (p2 + p - 2)
Multiply Trinomial and Binomial
Example 3: Multiply (4q2 - 2q + 8) and (2q + 5)
Example 4: Multiply (a + b - c) and (z + c)
Multiply Binomial and Trinomial
Example 1: Multiply (5a + b) and (a + b + c)
Solution: As per given question:
Binomial = (5a + b)
Trinomial = (a + b + c)
Write in the multiplication expression and we get:
(5a + b) (a + b + c)
Use Distributive Law and multiply each term of Bionomial with every term of trinomial & this is done in the following steps:
= (5a X a) +(5a X b) + (5a X c) + (b X a) +(b X b) + (b X c)
= 5a2 + 5ab + 5ac + ab + b2 + bc
Rearrange the terms as shown below:
= 5a2 + b2 + 5ab + ab + 5ac + bc
Add like terms (5ab + ab = 6ab) and we get:
= 5a2 + b2 + 6ab + 5ac + bc
Hence, (5a + b) (a + b + c) = 5a2 + b2 + 6ab + 5ac + bc
Example 2: Multiply (3p - 2) and (p2 + p - 2)
Solution: As per given question:
Binomial = (3p - 2)
Trinomial = (p2 + p - 2)
Write in the multiplication expression and we get:
(3p - 2) (p2 + p - 2)
Use Distributive Law and multiply each term of Bionomial with every term of trinomial & this is done in the following steps:
= (3p X p2) + (3p X p) - (3p X 2) - (2 X p2) - (2 X p) - (2 X -2)
= 3p3 + 3p2 - 6p - 2p2 - 2p - (-4)
Since [ -(-4) = 4], so we get:
= 3p3 + 3p2 - 6p - 2p2 - 2p + 4
Rearrange the terms as shown below:
= 3p3 + 3p2 - 2p2 - 6p - 2p + 4
Solve like terms and we get:
= 3p3 + p2 - 8p + 4
Hence, (3p - 2) (p2 + p - 2) = 3p3 + p2 - 8p + 4
Multiply Trinomial and Monomial
Example 3: Multiply (4q2 - 2q + 8) and (2q + 5)
Solution: As per given question:
Trinomial = (4q2 - 2q + 8)
Binomial = (2q + 5)
Write in the multiplication expression and we get:
(4q2 - 2q + 8) (2q + 5)
Use Distributive Law and multiply each term of Bionomial with every term of trinomial & this is done in the following steps:
= (4q2 X 2q) - (2q X 2q) + (8 X 2q) + (4q2 X 5) - (2q X 5) + (8 X 5)
= 8q3 - 4q2 + 16q + 20q2 - 10q + 40
Rearrange the terms as shown below:
= 8q3 - 4q2 + 20q2 + 16q - 10q + 40
Solve like terms and we get:
= 8q3 +16q2 + 6q + 40
Hence, (4q2 - 2q + 8) (2q + 5) = 8q3 + 16q2 + 6q + 40
Example 4: Multiply (a + b - c) and (z + c)
Solution: As per given question:
Trinomial = (a + b - c)
Binomial = z + c
Write in the multiplication expression and we get:
(a + b - c) (z + c)
Use Distributive Law and multiply each term of Bionomial with every term of trinomial & this is done in the following steps:
= (a X z) + (b X z) - (c X z) + (a X c) + (b X c) - (c X c)
= az + bz - cz + ac + bc - c2
Rearrange the terms as shown below:
= (- c2 + ac + az + bc + bz - cz)
Hence, (a + b - c) (z + c) = (- c2 + ac + az + bc + bz - cz)
|
|
