MULTIPLICATION OF POLYNOMIALS

About "multiplication of polynomials"

On this webpage "multiplication of polynomials", we are going to see how to multiply two or more polynomials with step by step explanation.

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 ( 5 x² ) and (-2 x³)

            =  ( 5 x² )  x (-2 x³)

            =  10 x

More examples of multiplication of polynomials

Problem 1

Multiply ( - 6 x ) and (- 4 x³)

         = ( - 6 x ) x (- 4 x³)

         =  24 x⁴

Problem 2

Multiply (2 a - 1) and  (8 a - 5)

         = (2 a - 1) (8 a - 5)

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

When we combine the like terms,we get

               = 16 a² - 18 a + 5

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

When we combine the like terms,we get

               = 16 a² - 18 a + 5

Problem 3

Multiply (2 a² + 5 a - 1) x (8 a² - 3 a + 5)

         = (2 a² + 5 a - 1) x (8 a² - 3 a + 5)

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

         = 16a⁴-6 a³+10 a²+40 a³-15 a²+25 a-8 a²+3 a-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 (2 x² + 5)  and (3y² - 4 y + 7)

         = (2 x² + 5) x (3y² - 4 y + 7)

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

      = 6 x²y² - 8 x² y + 14 x²+ 1 5 y² - 40 y + 35

now we have to combine the like terms

      = - 2 x² y + 14 x²+ 1 5 y² - 40 y + 35

Now let us see another problem in  multiplication of polynomials.

Problem 5

Multiply (3 x + 8)  and (4y - 7)

         = (3 x + 8) x (4y - 7)

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

               = 12 x y -21 x + 32 y - 56

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


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