Posted by Mimi on Tuesday, May 3, 2011 at 5:34pm.
Multiply:
(9t² - t- 7)(4t²+9t-1)
You can do a long multiplication, with the appropriate terms in the same columns, just like the multiplication of multi-digit numbers.
Alternatively, you can multiply visually, looking for highest to lowest terms:
t^4: 9*4 =36
t^3: 9*9+4(-1)=77
t^2: 9(-1)+(-1)(9)+(-7)(4)=-46
t: (-7)(9)+(-1)(-1)=-62
1: (-7)(-1) = 7
So the product is:
36t^4+77t^3-46t^2-62t+7
Quick check:
put t=1, so calculate the sum of coefficients of each factor:
(9t² - t- 7)(4t²+9t-1)
=(9-1-7)(4+9-1)
=1*12
=12
Sum of coefficients of product
=36+77-46-62+7
=12
checks.
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