The difference between the given expressions is \(2x^{3}-4x^{2}+24x-15\).
Given that, \((2x^{3}+9x-8)-(4x^{2} -15x+7)\).
We need to find the difference between the given expressions.
How to subtract the algebraic expression?
Steps to subtract algebraic expressions:
Step 1: Write all the expressions in a horizontal line by putting them into brackets and putting subtraction signs in between.
Step 2: Group all the like terms together from all the expressions and rewrite them into a single expression.
Step 3: Add numerical coefficients of all the like terms followed by the common variable.
Step 4: Rewrite the simplified expression, and make sure all the terms in the final answer are unlike terms.
Now, \((2x^{3}+9x-8)-(4x^{2} -15x+7)\),
\(=2x^{3}-4x^{2}+(9x+15x)-8-7\)
\(=2x^{3}-4x^{2}+24x-15\)
Therefore, the difference between the given expressions is \(2x^{3}-4x^{2}+24x-15\).
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