Answer:
To determine if the expressions \(5x^2 - 15\) and \(2x^2 - 4x + 7 - (3x^2 - 4x - 8)\) are equivalent, we first need to simplify the second expression.
Starting with:
\[ 2x^2 - 4x + 7 - (3x^2 - 4x - 8) \]
Distribute the negative sign across the terms in the parentheses:
\[ 2x^2 - 4x + 7 - 3x^2 + 4x + 8 \]
Now, combine like terms:
- Combine \(2x^2\) and \(-3x^2\):
\[ -x^2 \]
- Combine \(-4x\) and \(+4x\):
\[ 0x \]
- Combine \(7\) and \(8\):
\[ 15 \]
So, the simplified form of the second expression is:
\[ -x^2 + 15 \]
Comparing this with the first expression:
\[ 5x^2 - 15 \]
Clearly, the expressions are not equivalent as one is \(5x^2 - 15\) and the other is \(-x^2 + 15\). Thus, \(5x^2 - 15\) is not equivalent to \(2x^2 - 4x + 7 - (3x^2 - 4x - 8)\).
Step-by-step explanation:
