1. Find multiplication of `x^3-4x^2+4x-8` and `x-2`
Solution:
`(x^3-4x^2+4x-8) * (x-2)`
`=x^3*(x-2)-4x^2*(x-2)+4x*(x-2)-8*(x-2)`
`=x^4-2x^3-4x^3+8x^2+4x^2-8x-8x+16`
`=color{fuchsia}{ x^4}color{maroon}{ - 2x^3}color{maroon}{ - 4x^3}color{blue}{ + 8x^2}color{blue}{ + 4x^2}color{green}{ - 8x}color{green}{ - 8x}color{red}{ + 16}`
`=color{fuchsia}{ x^4}color{maroon}{ - 6x^3}color{blue}{ + 12x^2}color{green}{ - 16x}color{red}{ + 16}`
2. Find multiplication of `x^3+6x^2+12x+10` and `x+2`
Solution:
`(x^3+6x^2+12x+10) * (x+2)`
`=x^3*(x+2)+6x^2*(x+2)+12x*(x+2)+10*(x+2)`
`=x^4+2x^3+6x^3+12x^2+12x^2+24x+10x+20`
`=color{fuchsia}{ x^4}color{maroon}{ + 2x^3}color{maroon}{ + 6x^3}color{blue}{ + 12x^2}color{blue}{ + 12x^2}color{green}{ + 24x}color{green}{ + 10x}color{red}{ + 20}`
`=color{fuchsia}{ x^4}color{maroon}{ + 8x^3}color{blue}{ + 24x^2}color{green}{ + 34x}color{red}{ + 20}`
3. Find multiplication of `8x^3+10x-6` and `2x^2-4x+1`
Solution:
`(8x^3+10x-6) * (2x^2-4x+1)`
`=8x^3*(2x^2-4x+1)+10x*(2x^2-4x+1)-6*(2x^2-4x+1)`
`=16x^5-32x^4+8x^3+20x^3-40x^2+10x-12x^2+24x-6`
`=color{#FF6347}{ 16x^5}color{fuchsia}{ - 32x^4}color{maroon}{ + 8x^3}color{maroon}{ + 20x^3}color{blue}{ - 40x^2}color{green}{ + 10x}color{blue}{ - 12x^2}color{green}{ + 24x}color{red}{ - 6}`
`=color{#FF6347}{ 16x^5}color{fuchsia}{ - 32x^4}color{maroon}{ + 8x^3}color{maroon}{ + 20x^3}color{blue}{ - 40x^2}color{blue}{ - 12x^2}color{green}{ + 10x}color{green}{ + 24x}color{red}{ - 6}`
`=color{#FF6347}{ 16x^5}color{fuchsia}{ - 32x^4}color{maroon}{ + 28x^3}color{blue}{ - 52x^2}color{green}{ + 34x}color{red}{ - 6}`
This material is intended as a summary. Use your textbook for detail explanation.
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