a = x^2 - 4x + 8

\begin{array}{|c|c|c|c|}
\hline
x^2 & x^2 & x & x \\
\hline
x^2 & x^2 & x & x \\
\hline
x^2 & x^2 & x & x \\
\hline
x & x & 1 & 1 \\
\hline
\end{array}

Question

a = x^2 - 4x + 8

\begin{array}{|c|c|c|c|}
\hline
x^2 & x^2 & x & x \\
\hline
x^2 & x^2 & x & x \\
\hline
x^2 & x^2 & x & x \\
\hline
x & x & 1 & 1 \\
\hline
\end{array}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Algebraic Area Models", "Polynomial Multiplication", "Algebra Tiles" ], "current_concepts": [ "Algebraic Area Models", "Polynomial Multiplication", "Algebra Tiles" ] } ## Identificar las dimensiones del modelo de área $$ \begin{aligned} &\text{Ancho de las columnas (de izquierda a derecha): } x^2, \quad x, \quad 1, \quad 1 \ &\text{Ancho total} = x^2 + x + 2 \ &\text{Alto de las filas (de arriba a abajo): } x^2, \quad x, \quad x, \quad 1 \ &\text{Alto total} = x^2 + 2x + 1 \end{aligned} $$ ## Calcular el producto de los polinomios $$ \begin{aligned} P(x) &= (x^2 + x + 2)(x^2 + 2x + 1) \ &= x^2(x^2 + 2x + 1) + x(x^2 + 2x + 1) + 2(x^2 + 2x + 1) \ &= (x^4 + 2x^3 + x^2) + (x^3 + 2x^2 + x) + (2x^2 + 4x + 2) \end{aligned} $$ ## Simplificar sumando los términos semejantes $$ \begin{aligned} P(x) &= x^4 + (2 + 1)x^3 + (1 + 2 + 2)x^2 + (1 + 4)x + 2 \ &= x^4 + 3x^3 + 5x^2 + 5x + 2 \end{aligned} $$ $$(x^2 + x + 2)(x^2 + 2x + 1) = x^4 + 3x^3 + 5x^2 + 5x + 2$$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identificar las dimensiones del modelo de área

Calcular el producto de los polinomios

Simplificar sumando los términos semejantes

Answer: