# 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.  