Pregunta
\( \frac { ( 3 b ) ^ { 2 } + 12 a b ^ { 5 } } { 3 b } = \square b + \square a b \)
Ask by Ramirez Weber. in Canada
Mar 16,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\(3b + 4ab\).
Solución
To solve the equation
\[
\frac{(3b)^2 + 12ab^5}{3b} = \square b + \square ab,
\]
we will simplify the left-hand side step by step.
1. **Calculate \((3b)^2\)**:
\[
(3b)^2 = 9b^2.
\]
2. **Substitute this back into the equation**:
\[
\frac{9b^2 + 12ab^5}{3b}.
\]
3. **Separate the terms in the numerator**:
\[
\frac{9b^2}{3b} + \frac{12ab^5}{3b}.
\]
4. **Simplify each term**:
- For the first term:
\[
\frac{9b^2}{3b} = 3b.
\]
- For the second term:
\[
\frac{12ab^5}{3b} = 4ab^4.
\]
5. **Combine the simplified terms**:
\[
3b + 4ab^4.
\]
Now we can rewrite the equation as:
\[
3b + 4ab^4 = \square b + \square ab.
\]
From this, we can identify the coefficients:
- The coefficient of \(b\) is \(3\).
- The coefficient of \(ab\) is \(4b^3\) (since \(4ab^4\) can be expressed as \(4a b^4\)).
Thus, we can fill in the squares:
\[
\boxed{3} b + \boxed{4} ab.
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg


Bonus Knowledge
Let's break this down! When simplifying the expression \( \frac { ( 3 b ) ^ { 2 } + 12 a b ^ { 5 } } { 3 b } \), first, we can rewrite the numerator: \( (3b)^2 = 9b^2 \). Now, substituting this back, we have \( \frac { 9b^2 + 12ab^5 } { 3b } \). Next, we can separate the terms: \[ \frac{9b^2}{3b} + \frac{12ab^5}{3b} = 3b + 4ab^4. \] Thus, the expression simplifies to \( 3b + 4ab^4 \). So, filling in the squares, we have: \( \square = 3 \) and \( 4 \).
preguntas relacionadas

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium