Application of detached coefficient in multiplication
Example: Expand (2 – x + 3x3 – x4) by (1 – 2x2 + x3 + 2x5) up to the third power of X.
Answer:
We will omit all powers of x > 3 in the multiplication. Arranging in ascending order of power of x for multiplication by the method of detached coefficient;
Example: Expand (2 – x + 3x3 – x4) by (1 – 2x2 + x3 + 2x5) up to the third power of X.
Answer:
We will omit all powers of x > 3 in the multiplication. Arranging in ascending order of power of x for multiplication by the method of detached coefficient;
For multiplying (2 – x + 3x3 – x4) by (1 – 2x2 + x3
+ 2x5)
For using this method
the coefficients must be arranged in ascending or the descending order of power
of x. 0 as coefficient must be used for missing powers of x.
x0 x1 x2 x3 x4 x5 .............................. x9
2 -1 0 3 .. ..
1 0 -2 1 .. ..
2 -1 0 3 .. .. (multiplying 1with all the above numbers)
0 0 0 .. .. (multiplying 0
with all the above numbers)
-4 2 .. .. (multiplying
-2 with all the above numbers)
2 .. (multiplying 1 with all the above numbers)
2 -1 -4 7 are the coefficients of
rising power of x from left to right
Note we have restricted
all multiplications to x3. This will save tremendous amount of time
and effort.
So, the answer is
2 –x – 4x2 +
7x3
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