1. Find addition of `3x^2-10x+25` and `x^2+2x+2`

Solution:
`(3x^2-10x+25) + (x^2+2x+2)`

`=color{blue}{ 3x^2}color{green}{ - 10x}color{red}{ + 25}color{blue}{ + x^2}color{green}{ + 2x}color{red}{ + 2}` (Identify like terms)

`=color{blue}{ 3x^2}color{blue}{ + x^2}color{green}{ - 10x}color{green}{ + 2x}color{red}{ + 25}color{red}{ + 2}` (Rearrange terms to get like terms together)

`=color{blue}{ 4x^2}color{green}{ - 8x}color{red}{ + 27}` (Combine like terms)

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Method-2: Add using the Vertical method

	``	`3x^2`	`-`	`10x`	`+`	`25`
+	``	`x^2`	`+`	`2x`	`+`	`2`
	``	`4x^2`	`-`	`8x`	`+`	`27`

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2. Find addition of `4x^3-2x^2+x-8` and `x^3-4x^2-4x-1`

Solution:
`(4x^3-2x^2+x-8) + (x^3-4x^2-4x-1)`

`=color{maroon}{ 4x^3}color{blue}{ - 2x^2}color{green}{ + x}color{red}{ - 8}color{maroon}{ + x^3}color{blue}{ - 4x^2}color{green}{ - 4x}color{red}{ - 1}` (Identify like terms)

`=color{maroon}{ 4x^3}color{maroon}{ + x^3}color{blue}{ - 2x^2}color{blue}{ - 4x^2}color{green}{ + x}color{green}{ - 4x}color{red}{ - 8}color{red}{ - 1}` (Rearrange terms to get like terms together)

`=color{maroon}{ 5x^3}color{blue}{ - 6x^2}color{green}{ - 3x}color{red}{ - 9}` (Combine like terms)

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Method-2: Add using the Vertical method

	``	`4x^3`	`-`	`2x^2`	`+`	`x`	`-`	`8`
+	``	`x^3`	`-`	`4x^2`	`-`	`4x`	`-`	`1`
	``	`5x^3`	`-`	`6x^2`	`-`	`3x`	`-`	`9`

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3. Find addition 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}` (Identify like terms)

`=color{maroon}{ 8x^3}color{blue}{ + 2x^2}color{green}{ + 10x}color{green}{ - 4x}color{red}{ - 6}color{red}{ + 1}` (Rearrange terms to get like terms together)

`=color{maroon}{ 8x^3}color{blue}{ + 2x^2}color{green}{ + 6x}color{red}{ - 5}` (Combine like terms)

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Method-2: Add using the Vertical method

	``	`8x^3`	`+`	`0x^2`	`+`	`10x`	`-`	`6`
+			``	`2x^2`	`-`	`4x`	`+`	`1`
	``	`8x^3`	`+`	`2x^2`	`+`	`6x`	`-`	`5`

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4. Find addition of `6x^3+x^2+2x+6` and `x^3+4x^2-4x-16`

Solution:
`(6x^3+x^2+2x+6) + (x^3+4x^2-4x-16)`

`=color{maroon}{ 6x^3}color{blue}{ + x^2}color{green}{ + 2x}color{red}{ + 6}color{maroon}{ + x^3}color{blue}{ + 4x^2}color{green}{ - 4x}color{red}{ - 16}` (Identify like terms)

`=color{maroon}{ 6x^3}color{maroon}{ + x^3}color{blue}{ + x^2}color{blue}{ + 4x^2}color{green}{ + 2x}color{green}{ - 4x}color{red}{ + 6}color{red}{ - 16}` (Rearrange terms to get like terms together)

`=color{maroon}{ 7x^3}color{blue}{ + 5x^2}color{green}{ - 2x}color{red}{ - 10}` (Combine like terms)

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Method-2: Add using the Vertical method

	``	`6x^3`	`+`	`x^2`	`+`	`2x`	`+`	`6`
+	``	`x^3`	`+`	`4x^2`	`-`	`4x`	`-`	`16`
	``	`7x^3`	`+`	`5x^2`	`-`	`2x`	`-`	`10`

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5. Find addition of `x^4-4x^3-4x+4` and `x^4-x^2+2x-2`

Solution:
`(x^4-4x^3-4x+4) + (x^4-x^2+2x-2)`

`=color{fuchsia}{ x^4}color{maroon}{ - 4x^3}color{green}{ - 4x}color{red}{ + 4}color{fuchsia}{ + x^4}color{blue}{ - x^2}color{green}{ + 2x}color{red}{ - 2}` (Identify like terms)

`=color{fuchsia}{ x^4}color{fuchsia}{ + x^4}color{maroon}{ - 4x^3}color{blue}{ - x^2}color{green}{ - 4x}color{green}{ + 2x}color{red}{ + 4}color{red}{ - 2}` (Rearrange terms to get like terms together)

`=color{fuchsia}{ 2x^4}color{maroon}{ - 4x^3}color{blue}{ - x^2}color{green}{ - 2x}color{red}{ + 2}` (Combine like terms)

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Method-2: Add using the Vertical method

	``	`x^4`	`-`	`4x^3`	`+`	`0x^2`	`-`	`4x`	`+`	`4`
+	``	`x^4`	`+`	`0x^3`	`-`	`x^2`	`+`	`2x`	`-`	`2`
	``	`2x^4`	`-`	`4x^3`	`-`	`x^2`	`-`	`2x`	`+`	`2`

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