Q. \((-x)^2\)
Answer
\( (-x)^2 = (-1\cdot x)^2 = (-1)^2\cdot x^2 = 1\cdot x^2 = x^2 \).
Final result: \( x^2 \).
Detailed Explanation
We want to simplify the expression \( (-x)^2 \).
Step 1: Understand what the exponent means.
The exponent \(2\) means we multiply the quantity by itself:
\[
(-x)^2 = (-x)\cdot(-x)
\]
Step 2: Multiply the two factors.
Multiply the signs first and then the \(x\)-parts:
\((-x)\cdot(-x)\) has a negative times a negative, which gives a positive:
\[
(-x)\cdot(-x) = (+)\,x^2
\]
Step 3: Write the final simplified result.
\[
(-x)^2 = x^2
\]
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Algebra FAQ
Simplify \( (-x)^2 \).
\[ (-x)^2 = (-1)^2x^2 = x^2. \]
Why does the minus sign disappear in \( (-x)^2 \)?
\[ (-x)^2 = ((-1)x)^2 = (-1)^2x^2 = x^2. \] Squaring removes the sign.
What is \( (-x)^3 \) compared to \( (-x)^2 \)?
\[ (-x)^3 = (-1)^3x^3 = -x^3, \quad (-x)^2 = x^2. \]
Solve \( (-x)^2 = 9 \) for \(x\).
\[ (-x)^2 = x^2 = 9 \Rightarrow x = \pm 3. \]
Evaluate \( (-2x)^2 \).
\[ (-2x)^2 = (-1)^2(2x)^2 = 4x^2. \]
Simplify \( -(-x)^2 \).
\[ -(-x)^2 = -(x^2) = -x^2. \]
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