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Example 1
Add 4x4 + 3x3 - x2 + x + 6 and -7x4 - 3x3 + 8x2 + 8x - 4
We write them one below the other as shown below.
4x4 + 3x3 - x2 + x + 6
(+)
-7x4 - 3x3 + 8x2 + 8x - 4
-3x4 + 0 + 7x2 + 9x + 2
Example 2
Add 5x5 - 6x3 + 4x2 + 3x - 7, 3x5 - 2x4 + 3x2 + 6x - 1
and- 3x4 + x3 - 5x2 + 7x + 4
5x5 + - 6x3 + 4x2 + 3x - 7
3x5 - 2x4+ + 3x2 + 6x - 1
- 3x4+ x3 - 5x2 + 7x + 4
8x5 - 5x4 - 5x3 + 2x2 + 16x - 4
Example 3
Subtract -7x4 - 3x3+ 8x2 + 8x - 4 from 4x4 + 3x3 - x2 + x + 6
4x4 + 3x3- x2 + x + 6
(-)
11x4 + 6x3 - 9x2 - 7x + 10
In this problem, in some expressions we do not find terms of certain powers. They have been left as blanks.
Example 4
Subtract the first from the second and sum the difference with the third expression. The expressions are given below.
5x5 - 6x3 + 4x2 + 3x - 7, 3x5 - 2x4 + 3x2 + 6x - 1 and -3x4 + x3 - 5x2 + 7x + 4.
The difference of first two expressions is given by
3x5 - 2x4 + 3x2 + 6x - 1
5x5 - 6x3 + 4x2 + 3x - 7
-2x5 - 2x4 + 6x3 - x2 + 3x + 6
The sum of the difference between the first two expressions and the third expression will be as shown below.
(+) - 3x4+ x3 - 5x2 + 7x + 4
-2x5 - 5x4+ 7x3 - 6x2 + 10x + 10
number of consonants to the number of letters in the English Alphabet express answer in ratio
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
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