We want to find the following difference:
[tex](4x^5-3x^4+6x^2)-(7x^5-6x^4+x^3)[/tex]We just need to remember one rule: we can add or substract the terms if and only if the exponent of x is the same.
We distribute the parenthesis multiplication:
[tex]-(7x^5-6x^4+x^3)=-7x^5+6x^4-x^3[/tex]then
[tex]\begin{gathered} (4x^5-3x^4+6x^2)-(7x^5-6x^4+x^3) \\ =4x^5-3x^4+6x^2-7x^5+6x^4-x^3 \end{gathered}[/tex]We combine like terms
terms with x⁵: 4x⁵ and -7x⁵
terms with x⁴: -3x⁴ and 6x⁴
terms with x³: -x³
terms with x²: 6x²
We add them:
4x⁵ - 7x⁵ = -3x⁵
-3x⁴ + 6x⁴ = 3x⁴
-x³
6x²
Then,
[tex]\begin{gathered} (4x^5-3x^4+6x^2)-(7x^5-6x^4+x^3) \\ =-3x^5+3x^4-x^3+6x^2 \end{gathered}[/tex]
