Question
\( \left\lvert\, \leftarrow \begin{array}{l}\text { Perform the indicated operation and simplify. } \\ -(7 x-3)^{2} \\ -(7 x-3)^{2}=\square \text { (Simplify your answer.) }\end{array}\right. \)
Ask by Henry Hilton. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
-(7x - 3)^2 = -49x^2 + 42x - 9
\]
Solution
Para simplificar a expressão \( -(7x - 3)^2 \), siga os passos abaixo:
1. **Expanda o quadrado:**
\[
(7x - 3)^2 = (7x)^2 - 2 \cdot 7x \cdot 3 + (3)^2 = 49x^2 - 42x + 9
\]
2. **Aplique o sinal negativo:**
\[
-(7x - 3)^2 = -(49x^2 - 42x + 9) = -49x^2 + 42x - 9
\]
**Resposta simplificada:**
\[
-(7x - 3)^2 = -49x^2 + 42x - 9
\]
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Simplify this solution The Deep Dive
First, let's expand the expression \( -(7x - 3)^{2} \). We start by squaring \( (7x - 3) \): \[ (7x - 3)^{2} = 49x^{2} - 42x + 9. \] Now, applying the negative sign, we have: \[ -(7x - 3)^{2} = -49x^{2} + 42x - 9. \] So the simplified answer is: \[ \square = -49x^{2} + 42x - 9. \] Next, always double-check your signs during distribution and when applying negative signs! A common mistake might be dropping the negative when squaring or incorrectly applying it to individual terms. Remember, careful order of operations helps prevent mishaps!
