Question
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5) \( -3 e^{2}+4 f^{2}-c f^{2} \) b) \( -2 x b-7 a b+6 t \) h) \( 2 x y+5 x y-4 x y \) D \( \frac{1}{4} x^{2}-\frac{3}{x} x^{2}= \)

Ask by Bradley Rodriquez. in Mexico
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

5) \( -3e^{2} + 4f^{2} - cf^{2} \) b) \( -2xb - 7ab + 6t \) h) \( 3xy \) D) \( \frac{1}{4}x^{2} - 3x \)

Solution

Simplify the expression by following steps: - step0: Solution: \(-2xb-7ab+6t\) Calculate or simplify the expression \( 2 x y+5 x y-4 x y \). Simplify the expression by following steps: - step0: Solution: \(2xy+5xy-4xy\) - step1: Collect like terms: \(\left(2+5-4\right)xy\) - step2: Calculate: \(3xy\) Calculate or simplify the expression \( -3 e^{2}+4 f^{2}-c f^{2} \). Simplify the expression by following steps: - step0: Solution: \(-3e^{2}+4f^{2}-cf^{2}\) Calculate or simplify the expression \( \frac{1}{4} x^{2}-\frac{3}{x} x^{2} \). Simplify the expression by following steps: - step0: Solution: \(\frac{1}{4}x^{2}-\frac{3}{x}\times x^{2}\) - step1: Reduce the fraction: \(\frac{1}{4}x^{2}-3x\) Aquí están las simplificaciones de las expresiones que proporcionaste: 5) \( -3 e^{2}+4 f^{2}-c f^{2} \) se simplifica a: \[ -3e^{2}+4f^{2}-cf^{2} \] b) \( -2 x b-7 a b+6 t \) se simplifica a: \[ -2xb-7ab+6t \] h) \( 2 x y+5 x y-4 x y \) se simplifica a: \[ 3xy \] D) \( \frac{1}{4} x^{2}-\frac{3}{x} x^{2} \) se simplifica a: \[ \frac{1}{4}x^{2}-3x \]

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The Deep Dive

Let’s dive into these expressions! For the first expression \( -3 e^{2}+4 f^{2}-c f^{2} \), combine like terms involving \( f^2 \) to get \( (4 - c)f^{2} - 3e^{2} \). It’s always fun to combine terms and see the simplification come to life! Now, consider the expression \( -2 x b-7 a b+6 t \). Here, notice that while the terms \( -2xb \) and \( -7ab \) can be grouped by \( b \), the \( 6t \) doesn't share a factor, keeping it distinct. So, it simplifies to \( (-2xb - 7ab) + 6t \). It’s like piecing together a puzzle while ensuring every piece fits just right!

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