# 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.

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