Acceso
Prima
Hogar Banco de preguntas Matemáticas Álgebra
Pregunta
upstudy study bank question image url

\( 1 \& \quad \) Find the product. \( x(2 x+1)^{2} \) \( \begin{array}{l}x(2 x+1)^{2}=\square \\ (\text { Simplify your answer.) }\end{array} \)

Ask by Salinas West. in the United Arab Emirates
Mar 14,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

\( x(2x+1)^2 = 4x^3 + 4x^2 + x \)

Solución

¡Inicia sesión para desbloquear respuestas gratis!

Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

star-icon Descubrir

Respondido por UpStudy AI y revisado por un tutor profesional

Beyond the Answer

To find the product \( x(2x+1)^{2} \), let's first expand \( (2x+1)^{2} \). Using the formula \( (a+b)^{2} = a^{2} + 2ab + b^{2} \), where \( a = 2x \) and \( b = 1 \): \[ (2x+1)^{2} = (2x)^{2} + 2(2x)(1) + 1^{2} = 4x^{2} + 4x + 1. \] Now, substitute this back into the expression: \[ x(2x+1)^{2} = x(4x^{2} + 4x + 1). \] Next, distribute \( x \) into each term: \[ = 4x^{3} + 4x^{2} + x. \] So, the simplified expression is: \[ x(2x+1)^{2} = 4x^{3} + 4x^{2} + x. \] Thus, the final answer is \( \boxed{4x^{3} + 4x^{2} + x} \).

preguntas relacionadas

3. Write out Cayley tables for groups formed by the symmetries of a rectangle and for \( \left(\mathbb{Z}_{4 y},+\right) \). How many elements are in each group? Are the groups the same? Why or why not?
Álgebra United States Mar 17, 2025
Show instructions Question 1 (1 point) Using technology, find the roots of the polynomial equation: \[ f(x)=2 x^{2}+8.5 x+6.5 \] a \( \quad-\frac{2}{9},-1 \) b \( -\frac{13}{4},-1 \) c \( \frac{9}{8}, 17 \) d \( -\frac{2}{9}, 8 \) Question 2 (1 point) Using the rational roots theorem, list all the possible rational roots of \( f(x)=x^{3}-4 x^{2}+8 x-5 \) a \( \quad-5,-1,1,5 \) b \( \quad-5,-3-1,1,3,5 \) c \( -8,-5,-1,1,5,8 \) d none of the above Question 3 (1 point)
Álgebra United States Mar 17, 2025
Question 4 (1 point) State the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \( \begin{array}{l}x^{3}+3 x^{2}-x-3=0 \\ \text { a of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,-1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3, \text { double root at } 1\}\end{array} \) \( \begin{array}{l}\text { d }\end{array} \)
Álgebra United States Mar 17, 2025
Question 7 (1 point) State the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then finc all roots \[ x^{6}-x^{4}-x^{2}+1=0 \] a \# of complex roots: 6 Possible \# of real roots: \( 6,4,2 \), or 0 Possible \# of imaginary roots: \( 6,4,2 \), or 0 Possible rational roots: \( \pm 1 \) Roots: \( \{-1, i,-i\} \) b \# of complex roots: 6 Possible \# of real roots: \( 6,4,2 \), or 0 Possible \# of imaginary roots: \( 6,4,2 \), or 0 Possible rational roots: \( \pm 1 \) Roots: \( \{1 \) mult. \( 2,-1 \) mult. \( 2, i,-i\} \) c \# of complex roots: 6 Possible \# of real roots: \( 6,4,2 \), or 0 Possible \# of imaginary roots: \( 6,4,2 \), or 0 Possible rational roots: \( \pm 1 \) Roots: \( \{1 \) mult. 2, -1 mult. 2\} d \# of complex roots: 6 Possible \# of real roots: \( 6,4,2 \), or 0 Possible \# of imaginary roots: \( 6,4,2 \), or 0 Possible rational roots: \( \pm 1 \) Roots: \( \{1,-1,-2,2, i,-i\} \) Review Answers
Álgebra United States Mar 17, 2025
Question 6 (1 point) state the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \[ x^{3}-2 x^{2}-3 x+6=0 \] a \# of complex roots: 6 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots: \( -1, \pm \sqrt{3} \) b \# of complex roots: 6 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots: \( 2, \pm \sqrt{3} \) c \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots \( 2, \pm \sqrt{3} \) d \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots: \( -1, \pm \sqrt{3} \)
Álgebra United States Mar 17, 2025

Latest Algebra Questions

3. Write out Cayley tables for groups formed by the symmetries of a rectangle and for \( \left(\mathbb{Z}_{4 y},+\right) \). How many elements are in each group? Are the groups the same? Why or why not?
Álgebra United States Mar 17, 2025
himpunan penyelesaian dari sistem persamaan \( 2 x+2 y=4 \) dan \( 3 x+y=6 \) adalah
Álgebra Indonesia Mar 17, 2025
Question 4 (1 point) State the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \( \begin{array}{l}x^{3}+3 x^{2}-x-3=0 \\ \text { a of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,-1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3, \text { double root at } 1\}\end{array} \) \( \begin{array}{l}\text { d }\end{array} \)
Álgebra United States Mar 17, 2025
Summarize all pertinent information obtained by applying the graphing strategy and sketch the graph of \( y=f(x) \). \[ f(x)=\frac{x^{2}+13 x+36}{x^{2}+8 x+16} \] tina the aomain or \( \mathrm{r}(\mathrm{X}) \). seiect the correct cnoice deiow ana, it necessary, till in the answer dox to complete your cnoice. A. The domain is all real \( x \), except \( x= \) \( \square \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The domain is all real \( x \). Find the \( x \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( x \)-intercept(s) is/are at \( x= \) \( \square \) . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts. Find the \( y \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Álgebra United States Mar 17, 2025
State the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \[ x^{3}-1=0 \] a \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) \[ \text { Roots: } \pm 1, \frac{-1+i \sqrt{3}}{2} \] b \[ 1, \frac{-1+i \sqrt{3}}{2}, \frac{-1-i \sqrt{3}}{2} \text { \# of complex roots: } 3 \] Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) Roots: c \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) \[ \text { Roots: }-1, \frac{-1+i \sqrt{2}}{5}, \frac{-1-i \sqrt{2}}{5} \] d \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) Roots: \[ -1, \frac{i \sqrt{3}}{2}, \frac{-i \sqrt{3}}{2} \]
Álgebra United States Mar 17, 2025
Anterior Próximo
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad