Question

Simplify.
(3x5+3x2−4x3+x−6)−(x3+4x4+2x2−10x)

Answer 1

To simplify the given expression, distribute the negative sign, combine like terms, and simplify each group. The simplified expression is -x^5 - 8x^4 - 3x^3 + x^2 + 11x - 6.

Step-by-step explanation:

To simplify the given expression (3x^5+3x^2-4x^3+x-6)-(x^3+4x^4+2x^2-10x), we need to combine like terms and perform the necessary operations.

1. Distribute the negative sign inside the second set of parentheses: (-1)(x^3+4x^4+2x^2-10x) = -x^3-4x^4-2x^2+10x
2. Combine the like terms: 3x^5-4x^4-4x^3+3x^2+x-6-x^3-4x^4-2x^2+10x
3. Group the like terms together: (3x^5-4x^5) + (-4x^4-4x^4) + (-4x^3+x^3) + (3x^2-2x^2) + (x+10x) - 6
4. Simplify each group: -x^5 - 8x^4 - 3x^3 + x^2 + 11x - 6

The simplified expression is -x^5 - 8x^4 - 3x^3 + x^2 + 11x - 6.