%2B3x%5E(2)-2x%2B8)--(3x-2).jpeg "(27x^(3)+3x^(2)-2x+8)- (3x-2)")
Simplifying the Expression: (27x^(3)+3x^(2)-2x+8)- (3x-2)
This expression involves subtracting a binomial from a polynomial. To simplify this, we'll distribute the negative sign and then combine like terms.
Step 1: Distribute the Negative Sign
The negative sign in front of the parentheses means we multiply each term inside the parentheses by -1.
(27x^(3) + 3x^(2) - 2x + 8) - (3x - 2) becomes 27x^(3) + 3x^(2) - 2x + 8 - 3x + 2
Step 2: Combine Like Terms
Now we identify and combine terms with the same variable and exponent:
- x^(3) terms: 27x^(3)
- x^(2) terms: 3x^(2)
- x terms: -2x - 3x = -5x
- Constant terms: 8 + 2 = 10
Simplified Expression
Putting it all together, the simplified expression is:
27x^(3) + 3x^(2) - 5x + 10