🧮 algebra

1. Let's create an equation where all terms cancel out at the end. 2. Consider the equation $$\frac{x^2 - 1}{x - 1} = x + 1$$.

1. **State the problem:** We are given that \((2x + 3)\) is a factor of the cubic polynomial \(4x^3 - 12x^2 - 7x + 30\). We need to find all three solutions to the equation \(4x^3

1. **State the problem:** Multiply out and simplify the expression $$(4x - 10\sqrt{x})(2x + 5\sqrt{x} - 7).$$ 2. **Recall the distributive property:** To multiply two expressions,

1. **Problem statement:** (a) Find the highest common factor (HCF) of $5A$ and $2B$ given:

1. **State the problem:** Find the value of $k$ for which the system of equations $$\begin{cases} kx - y = 2 \\ 6x - 2y = 3 \end{cases}$$

1. **State the problem:** Find the equation of the perpendicular bisector of the line segment AB where A = (17,9) and B = (23,39). 2. **Formula and rules:**

1. **State the problem:** Simplify or analyze the quadratic expression $$x^2 - 4dx + 2d^2$$ where $x$ and $d$ are variables. 2. **Recall the quadratic form:** A quadratic expressio

1. Il problema richiede di risolvere l'equazione quadratica $$x^2 - 4x + 2p^2 = 0$$ dove $p$ è una costante. 2. La formula generale per risolvere un'equazione quadratica $$ax^2 + b

1. **State the problem:** Find the value of $k$ for which the system of equations $$kx - y = 2$$

1. **State the problem:** We have a pipe network with nodes E, D, A, B, C and flows $x_1$ through $x_6$ between them. Inputs are 200 at E, 150 at D, 25 at A, and output is 200 at C

1. **Problema 4: Identificar les antiimatges de la funció $f(x) = 3x + 2$ per a diferents valors de $y$.** 2. La funció és $f(x) = 3x + 2$. Per trobar l'antiimatge d'un valor $y$,

1. **Calcula la imatge f(x) per a cada valor de x** **a.** $f(x) = 2x + 1$

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **Stating the problem:** Simplify the expression $$L = \frac{7}{6} \times \left(\frac{7}{2} - \frac{3}{2}\right)$$. 2. **Apply the subtraction inside the parentheses:**

1. **Énoncé du problème :** Calculer les expressions données en respectant les priorités opératoires et simplifier les résultats sous forme de fractions. 2. **Rappel des règles imp

1. **Énoncé du problème :** Résoudre l'inéquation $x^2 - 3x + 2 > 0$. 2. **Formule et règle utilisée :** Pour résoudre une inéquation polynomiale du second degré, on commence par t

1. Das Problem: Wir sollen eine Gleichung oder ein Problem mit einer Formel lösen. Da keine konkrete Aufgabe gegeben ist, erkläre ich, wie man eine allgemeine Formel anwendet. 2. F

1. The problem asks how we know that $4^3 = 64$. 2. The expression $4^3$ means $4$ multiplied by itself 3 times: $4 \times 4 \times 4$.

1. The problem asks to find the cube root of 64, written as $\sqrt[3]{64}$.\n\n2. The cube root of a number $x$ is a value $y$ such that $y^3 = x$.\n\n3. We want to find $y$ such t

1. **State the problem:** Explain how to factor the expression $x^2 - 25$ into $(x - 5)(x + 5)$. 2. **Recall the difference of squares formula:** For any two terms $a$ and $b$, the

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Recall the division rule for fractions:** Dividing by a