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`