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 x⁵
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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