MULTIPLICATION OF POLYNOMIALS

Procedure of Multiplying Two Polynomials

We will multiply two or more polynomials in the following order.

(1) Symbol

(2) Number

(3) Variable

Let us see how it works

Multiply (5x²) and (-2x³)

  =  (5x²) (-2x³)

 10 x

More Examples of Multiplication of Polynomials

Problem 1 :

Multiply (-6x) and (-4x³)

Solution :

  =  (-6x) x (-4x³)

  =   24 x⁴

Problem 2 :

Multiply (2a-1) and  (8a-5)

Solution :

  =  (2a-1) (8a-5)

To multiply these binomials we have to distribute 2a with (8a-5) and distribute -1 with (8a-5)

When we combine the like terms,we get

  =  16a²-18a+5

We can do the the same problem in the following flow chart method also.

When we combine the like terms,we get

  =  16a²-18a+5

Problem 3 :

Multiply (2a²+5a-1) (8a²-3a+5)

Solution :

  =  (2a²+5a-1) (8a²-3a+5)

To multiply these trinomials, we have to distribute 2 a² with  (8a²-3a+5), distribute 5a with  (8a²-3a+5) and -1 with  (8 a² - 3 a + 5).

  =  16a⁴-6a³+10a²+40a³-15a²+25a-8a²+3a-5

Now we have to combine the like terms

  =  16a⁴-6a³+40a³+10a²-15a²-8a²+25a+3a-5

  =  16a⁴ + 34 a³ -13 a²+ 28 a - 5

Problem 4 :

Multiply (2x²+5)  and (3y²-4y+7)

Solution :

  =  (2x²+5) (3y²-4y+7)

To multiply these binomial and trinomial we have to distribute 2x² with  (3y²-4y+7) and distribute 5 with  (3y²-4y+7).

  =  6x²y²-8x²y+14x²+15y²-40y+35

now we have to combine the like terms

=  -2x²y+14x²+15y²-40y+35

Problem 5 :

Multiply (3x+8)  and (4y-7)

Solution :

  =  (3x+8)(4y-7)

To multiply these binomials we have to distribute 3x with  (4y-7) and distribute 8 with (4y-7)

  =  12xy-21x+32y-56

Since there is no like terms. So we cannot simplify this.

Related Pages

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Cross Product Rule in Proportion

    Oct 05, 22 11:41 AM

    Cross Product Rule in Proportion - Concept - Solved Problems

    Read More

  2. Power Rule of Logarithms

    Oct 04, 22 11:08 PM

    Power Rule of Logarithms - Concept - Solved Problems

    Read More

  3. Product Rule of Logarithms

    Oct 04, 22 11:07 PM

    Product Rule of Logarithms - Concept - Solved Problems

    Read More