1. Find Subtraction of `8x^3+10x-6` and `2x^2-4x+1`
Solution:
`(8x^3+10x-6) - (2x^2-4x+1)`
`=color{maroon}{ 8x^3}color{green}{ + 10x}color{red}{ - 6}color{blue}{ - 2x^2}color{green}{ + 4x}color{red}{ - 1}`
`=color{maroon}{ 8x^3}color{blue}{ - 2x^2}color{green}{ + 10x}color{green}{ + 4x}color{red}{ - 6}color{red}{ - 1}`
`=color{maroon}{ 8x^3}color{blue}{ - 2x^2}color{green}{ + 14x}color{red}{ - 7}`
OR
| `` | `8x^3` | `+` | `0x^2` | `+` | `10x` | `-` | `6` |
| - | | | `` | −`2x^2` | `-` | +`4x` | `+` | −`1` |
|
| `` | `8x^3` | `-` | `2x^2` | `+` | `14x` | `-` | `7` |
2. Find Subtraction of `x^4-4x^3-4x+4` and `x^2+2x-2`
Solution:
`(x^4-4x^3-4x+4) - (x^2+2x-2)`
`=color{fuchsia}{ x^4}color{maroon}{ - 4x^3}color{green}{ - 4x}color{red}{ + 4}color{blue}{ - x^2}color{green}{ - 2x}color{red}{ + 2}`
`=color{fuchsia}{ x^4}color{maroon}{ - 4x^3}color{blue}{ - x^2}color{green}{ - 4x}color{green}{ - 2x}color{red}{ + 4}color{red}{ + 2}`
`=color{fuchsia}{ x^4}color{maroon}{ - 4x^3}color{blue}{ - x^2}color{green}{ - 6x}color{red}{ + 6}`
OR
| `` | `x^4` | `-` | `4x^3` | `+` | `0x^2` | `-` | `4x` | `+` | `4` |
| - | | | | | `` | −`x^2` | `+` | −`2x` | `-` | +`2` |
|
| `` | `x^4` | `-` | `4x^3` | `-` | `x^2` | `-` | `6x` | `+` | `6` |
3. Find Subtraction of `x^3+4x^2-4x-16` and `x-2`
Solution:
`(x^3+4x^2-4x-16) - (x-2)`
`=color{maroon}{ x^3}color{blue}{ + 4x^2}color{green}{ - 4x}color{red}{ - 16}color{green}{ - x}color{red}{ + 2}`
`=color{maroon}{ x^3}color{blue}{ + 4x^2}color{green}{ - 4x}color{green}{ - x}color{red}{ - 16}color{red}{ + 2}`
`=color{maroon}{ x^3}color{blue}{ + 4x^2}color{green}{ - 5x}color{red}{ - 14}`
OR
| `` | `x^3` | `+` | `4x^2` | `-` | `4x` | `-` | `16` |
| - | | | | | `` | −`x` | `-` | +`2` |
|
| `` | `x^3` | `+` | `4x^2` | `-` | `5x` | `-` | `14` |
This material is intended as a summary. Use your textbook for detail explanation.
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