To solve the given expression [tex]\( 2x^2 - x^2 \)[/tex], let’s break it down step by step:
1. Identify the terms in the expression:
- The first term is [tex]\( 2x^2 \)[/tex].
- The second term is [tex]\( -x^2 \)[/tex].
2. Combine like terms:
- Both terms involve [tex]\( x^2 \)[/tex], so they are like terms and can be combined.
- When combining like terms, simply add or subtract the coefficients of the terms.
3. Calculate the result:
- The coefficient of the first term is 2, and the coefficient of the second term is -1.
- Therefore, combining these like terms:
[tex]\[
2x^2 - x^2 = (2 - 1)x^2 = 1x^2 = x^2
\][/tex]
Thus, the given expression [tex]\( 2x^2 - x^2 \)[/tex] simplifies to [tex]\( x^2 \)[/tex].
4. Compare with the given options:
- Option 1: [tex]\( x^0 \)[/tex] is not equivalent to [tex]\( x^2 \)[/tex].
- Option 2: 2 is not equivalent to [tex]\( x^2 \)[/tex].
- Option 3: [tex]\( x^2 \)[/tex] is exactly what we found.
- Option 4: [tex]\( -2x^4 \)[/tex] is not equivalent to [tex]\( x^2 \)[/tex].
The correct option is:
(3) [tex]\( x^2 \)[/tex]
