🧮 algebra

1. **State the problem:** Simplify and analyze the expression $(a + 3\sqrt{5})^2 + a - b\sqrt{5} - 51$ and compare it to the expanded forms given. 2. **Expand the square:**

1. **State the problem:** Evaluate the function $f(x) = x^3 - 9x^2 + 24x - 18$ at $x = -1$ and analyze its properties. 2. **Calculate $f(-1)$:**

1. **Évaluer l'expression** $((\sqrt{2024} - 13)^0 - 2)^{2023}$ On sait que toute expression élevée à la puissance 0 vaut 1, sauf si la base est 0.

1. Stating the problem: We want to decompose the rational expression \(\frac{x+3}{(x-2)^2}\) into partial fractions. 2. Since the denominator is \((x-2)^2\), the partial fraction d

1. **Problem:** Lösen Sie die Gleichung $$\frac{1}{a} = \frac{1}{b} + \frac{1}{c}$$ nach $$a$$ auf. 2. Zuerst bringen wir die rechte Seite auf einen gemeinsamen Nenner:

1. The problem is to simplify or resolve the expression $x+\frac{3}{(x-2)^2}$.\n\n2. Since the terms are not combined under a single denominator, rewrite the expression with a comm

1. Problem statement: Analyze the function $f(x) = x^3 - 9x^2 + 24x - 18$ in terms of domain, range, intercepts, limits, derivatives, and continuity.\n\n2. Domain: Since $f(x)$ is

1. The problem is to find the domain of the function $$f(x) = \frac{1}{\sqrt{2x-4}}$$. 2. Start by identifying the domain restrictions. Since the denominator is a square root, the

1. The problem is to solve for $x$ given the equation $2x + 3 = 7$. 2. Start by isolating $x$ on one side of the equation. Subtract 3 from both sides:

1. Let's state the problem: Given the exercise number 1 as an example, we need to show how to solve it. 2. Since the problem details are not provided, let's assume a basic example

1) Calculer : 1. Calcul de A = $(-\sqrt{25})^2$\: \rightarrow -\sqrt{25} = -5$ donc $A = (-5)^2 = 25$.

1. Stating the problem: We want to decompose the rational expression $$\frac{x+3}{(x-2)^2}$$ into partial fractions. 2. Because the denominator has a repeated linear factor $(x-2)^

1. **State the problem:** We need to analyze the inequality $y \leq x + 2$. 2. **Rewrite the inequality:** It says that the value of $y$ is less than or equal to the value of the e

1. El problema consiste en realizar varias operaciones de división y multiplicación con números en notación científica. 2. Recordemos la regla básica para dividir potencias con bas

1. Given the expression to decompose: $$x + \frac{3}{(x - 2)^2}$$ 2. Since the denominator is $(x - 2)^2$, consider partial fractions of the form: $$\frac{A}{x - 2} + \frac{B}{(x -

1. The problem is to graph the linear inequality $y > 1$. 2. This inequality means we want all points where the $y$-coordinate is greater than 1.

1. We are asked to simplify or resolve the expression $x + \frac{3}{(x - 2)^2}$. 2. The expression consists of two terms: $x$, which is a linear term, and $\frac{3}{(x - 2)^2}$, wh

1. Let's clarify what a graph is in math: It is a visual representation of a function or equation showing how variables relate. 2. If you provide your specific equation or function

1. The problem is to analyze and describe the graph of the function given by $$y = (x - 8)^2 - 6$$. 2. This is a quadratic function in vertex form: $$y = (x - h)^2 + k$$ where \(h

1. נתונה הפונקציה: $f(x)=(x+1)\cdot e^x$. 2. נמצא את תחום ההגדרה של הפונקציה:

1. Énoncé du problème : Il s'agit de factoriser les expressions suivantes : M = (4 + x)^2 - (2x + 8)(x - 2)