Pregunta
Multiply. \[ (5 x-2 z)(7 x+z) \] Simplify your answer.
Ask by Nichols Jimenez. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( 35x^2 - 9xz - 2z^2 \)
Solución
To multiply and simplify the expression \((5x - 2z)(7x + z)\), follow these steps:
1. **Apply the Distributive Property (FOIL Method):**
\[
\begin{align*}
(5x - 2z)(7x + z) &= 5x \cdot 7x + 5x \cdot z - 2z \cdot 7x - 2z \cdot z \\
&= 35x^2 + 5xz - 14xz - 2z^2
\end{align*}
\]
2. **Combine Like Terms:**
\[
35x^2 + (5xz - 14xz) - 2z^2 = 35x^2 - 9xz - 2z^2
\]
**Simplified Answer:**
\[
35x^2 - 9xz - 2z^2
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To multiply the expressions \( (5x - 2z)(7x + z) \), we'll use the distributive property (also known as the FOIL method for binomials). 1. First, multiply \( 5x \) by \( 7x \): \[ 5x \cdot 7x = 35x^2 \] 2. Next, multiply \( 5x \) by \( z \): \[ 5x \cdot z = 5xz \] 3. Then, multiply \( -2z \) by \( 7x \): \[ -2z \cdot 7x = -14xz \] 4. Finally, multiply \( -2z \) by \( z \): \[ -2z \cdot z = -2z^2 \] Now, combine all these results: \[ 35x^2 + 5xz - 14xz - 2z^2 \] Combine the like terms \( 5xz - 14xz \): \[ 35x^2 - 9xz - 2z^2 \] So, the simplified answer is: \[ \boxed{35x^2 - 9xz - 2z^2} \]
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