Questions: In the indicated operation by removing the parentheses and combining like terms. [ (-3 x^2+2 x-5)-(-7 x^2+1) ]

In the indicated operation by removing the parentheses and combining like terms. [ (-3 x^2+2 x-5)-(-7 x^2+1) ]
Transcript text: n the indicated operation by removing the parentheses and combining like terms. \[ \left(-3 x^{2}+2 x-5\right)-\left(-7 x^{2}+1\right) \]
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Solution

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Solution Steps

Step 1: Remove the Parentheses

Start by removing the parentheses. Remember to distribute the negative sign to each term inside the second set of parentheses: \[ \left(-3x^{2} + 2x - 5\right) - \left(-7x^{2} + 1\right) = -3x^{2} + 2x - 5 + 7x^{2} - 1 \]

Step 2: Combine Like Terms

Combine the terms that have the same variable and exponent: \[ -3x^{2} + 7x^{2} + 2x - 5 - 1 \]

Step 3: Simplify the Expression

Perform the arithmetic operations on the like terms: \[ (-3x^{2} + 7x^{2}) + 2x + (-5 - 1) = 4x^{2} + 2x - 6 \]

Final Answer

\(\boxed{4x^{2} + 2x - 6}\)

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