Example 1
Add 4x^{4} + 3x^{3} - x^{2} + x + 6 and -7x^{4} - 3x^{3} + 8x^{2} + 8x - 4
We write them one below the other as shown below.
4x^{4} + 3x^{3} - x^{2} + x + 6
(+)
-7x^{4} - 3x^{3} + 8x^{2} + 8x - 4
-3x^{4} + 0 + 7x^{2} + 9x + 2
Example 2
Add 5x^{5} - 6x^{3} + 4x^{2} + 3x - 7, 3x^{5} - 2x^{4} + 3x^{2} + 6x - 1
and- 3x^{4} + x^{3} - 5x^{2} + 7x + 4
5x^{5} + - 6x^{3} + 4x^{2} + 3x - 7
3x^{5} - 2x^{4}+ + 3x^{2} + 6x - 1
- 3x^{4}+ x^{3} - 5x^{2} + 7x + 4
8x^{5} - 5x^{4} - 5x^{3} + 2x^{2} + 16x - 4
Example 3
Subtract -7x^{4} - 3x^{3}+ 8x^{2} + 8x - 4 from 4x^{4} + 3x^{3} - x^{2} + x + 6
4x^{4 }+ 3x^{3}- x^{2} + x + 6
(-)
-7x^{4 }- 3x^{3} + 8x^{2} + 8x - 4
11x^{4 }+ 6x^{3} - 9x^{2} - 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.
5x^{5} - 6x^{3} + 4x^{2} + 3x - 7, 3x^{5} - 2x^{4} + 3x^{2 }+ 6x - 1 and -3x^{4 }+ x^{3 }- 5x^{2 }+ 7x + 4.
The difference of first two expressions is given by
3x^{5} - 2x^{4} + 3x^{2} + 6x - 1
5x^{5 }- 6x^{3} + 4x^{2} + 3x - 7
-2x^{5} - 2x^{4} + 6x^{3} - x^{2} + 3x + 6
The sum of the difference between the first two expressions and the third expression will be as shown below.
(+) - 3x^{4}+ x^{3} - 5x^{2} + 7x + 4
-2x^{5} - 5x^{4}+ 7x^{3} - 6x^{2} + 10x + 10