🧮 algebra

1. **State the problem:** Simplify the expression $$\ln\left(\frac{\sqrt[3]{x^2}}{w+z}\right)$$. 2. **Recall the logarithm property:** For any positive values, $$\ln\left(\frac{a}{

1. **State the problem:** Write the logarithmic expressions as exponential expressions. 2. **Recall the logarithm to exponential conversion formula:**

1. Beseitige die Klammern und fasse so weit wie möglich zusammen: 1.a) \((a-b) - (a+b) - (b-a)\)

1. **State the problem:** Simplify the expression $$\frac{5}{2 - \sqrt{2}}$$. 2. **Formula and rule:** To simplify expressions with radicals in the denominator, multiply numerator

1. **Problem 9:** Simplify $-\sqrt{6}n(\sqrt{6} + 2)$. 2. Use the distributive property: $-\sqrt{6}n \times \sqrt{6} + (-\sqrt{6}n) \times 2$.

1. **Problem statement:** Calculate the expansion of the expression $ (2x+3)^5 $. 2. **Formula used:** We use the Binomial Theorem, which states:

1. **Terme zusammenfassen** **a)** $15x - 6y - 2x + 4y$

1. **State the problem:** Given the polynomial equation $$x^4 + 2x^3 - 10x^2 - 18x + 9 = 0$$, we need to:

1. **State the problem:** Solve the polynomial equation $$x^4 + 4x^3 - 3x^2 - 16x - 4 = 0$$ given that one rational root is $$x = -2$$. 2. **Use synthetic division to divide the po

1. **Enunciato del problema:** Determina l'equazione della parabola con fuoco $F(1, -\frac{3}{2})$ e vertice $V(1, -2)$.

1. **State the problem:** Simplify or analyze the expression $2x^3 + 6x^2 - 1$. 2. **Identify the type of expression:** This is a cubic polynomial.

1. **State the problem:** Simplify the expression $$\frac{320yx}{20x^{2}yx}$$. 2. **Write the formula and rules:** When simplifying fractions, divide numerator and denominator by t

1. **State the problem:** Simplify or analyze the polynomial expression $2x^3 - 6x + 1$. 2. **Identify the type of expression:** This is a cubic polynomial with terms $2x^3$, $-6x$

1. **State the problem:** We need to find the element in the 3rd row and 2nd column of the product matrix $AB$, denoted as $(AB)_{3,2}$. 2. **Recall matrix multiplication rule:** T

1. **Problemstellung:** Gegeben ist die proportionale Funktion $f(x) = \frac{1}{2}x$. Zeichne den Graphen mit Hilfe einer Wertetabelle. 2. **Formel und Regeln:** Eine proportionale

1. **Enunciato del problema:** Traccia il grafico della parabola data dall'equazione $$y = x^2 - 6x - 2$$ e determina l'area del triangolo formato dai suoi punti di intersezione co

1. Il problema chiede di trovare il vertice e altri 4 punti della parabola data dalla funzione $$y = x^2 - 2x - 4$$. 2. La formula per trovare il vertice di una parabola $$y = ax^2

1. **State the problem:** Solve the system of equations algebraically: $$x - 2y + 2 = 0$$

1. **State the problem:** Solve for the variable $w$ in the equation $35 - 12w = 29$. 2. **Isolate the term with the variable:** Subtract 35 from both sides to get the term with $w

1. **Problem:** Solve the equation $\frac{1}{2}x + \frac{3}{2}(x+1) - \frac{1}{4} = 5$. 2. **Use the distributive property first.**

1. **State the problem:** Solve the equation $$x^{\sqrt{x}} = 10$$ for $x$. 2. **Rewrite the equation:** Let $y = \sqrt{x}$. Then $x = y^2$. Substitute into the equation: