Final answer:
To simplify the given expression, expand the parentheses, combine like terms, and then subtract and combine the resulting terms to obtain the simplified expression 9x^4 - 8x^2 + 4x.
Step-by-step explanation:
To simplify the expression (2x^4-3x)(x+2) - (x+2)(5x-5x^4), we need to perform the following steps:
- Expand the parentheses.
- Combine like terms.
- Simplify the resulting expression.
Expanding the parentheses, we get:
(2x^4)(x) + (2x^4)(2) - (3x)(x) - (3x)(2) for the first part and (x)(5x) - (x)(5x^4) + (2)(5x) - (2)(5x^4) for the second part.
Then we combine like terms:
(2x^5 + 4x^4 - 3x^2 - 6x) - (5x^2 - 5x^5 + 10x - 10x^4).
Finally, we simplify the expression by subtracting and combining all like terms, resulting in:
9x^4 - 8x^2 + 4x.
Equations can vary in complexity, involving multiple variables, powers, trigonometric functions, and more. Solving equations often requires using algebraic techniques, such as factoring, combining like terms, applying properties of equality, or using specific methods tailored to the equation's form to find the solution(s).