🧮 algebra

1. **State the problem:** Factorise completely the expression $14xy - 7y^2$ using the factorising method. 2. **Identify common factors:** Look for the greatest common factor (GCF)

1. **State the problem:** Solve the quadratic equation $X^2 + 8X + 10 = 30$ using the factorising method. 2. **Rewrite the equation:** Move all terms to one side to set the equatio

1. **Problemstellung:** Untersuchen Sie die Funktion $f(x)=0,5x^2-4x$ bezüglich Symmetrie, Globalverhalten, Achsenschnittpunkten, lokalen Extrem- und Wendepunkten sowie Steigungs-

1. Das Problem: Löse die Gleichung $11x - 7 = 4x + 18$. 2. Formel und Regeln: Um eine lineare Gleichung zu lösen, bringen wir alle Terme mit $x$ auf eine Seite und die Konstanten a

1. **Problemstellung:** Löse die quadratische Funktion $f(x)=0,5x^2-4x$ und untersuche sie bezüglich Symmetrie, Achsenschnittpunkten, Extremstellen und Krümmungsverhalten. 2. **For

1. **State the problem:** Solve the quadratic equation $$3x^2 = 4 - 4x$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to find the value of $r$ given an equation involving $r$. However, the equation is missing from the user's message. 2. To solve for $r$, we need the full equation

1. **State the problem:** Solve the linear equation $$22 - 8x = 2x + 9$$ for $x$. 2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of t

1. **State the problem:** Solve the linear equation $4m + 5 = 35 - 2m$ for $m$. 2. **Write down the equation:**

1. **Problem statement:** Vi har funktionen $$f(x) = \frac{1}{3}x^3 - 2x^2 - 5x + 8$$.

1. **State the problem:** Evaluate the expression $(-3)^2 - (-1)^3$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{18h^2}{9h}$$. 2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} =

1. The problem is to evaluate powers of negative numbers and understand their results. 2. The formula for powers is $a^n = a \times a \times \cdots \times a$ ($n$ times).

1. Let's start with problem (a): Find the set $A_1 = \{x \in \mathbb{Z} : 2x^2 - 3 = x\}$. 2. Rearrange the equation:

1. Planteamos el problema: Encontrar los valores de $A$ y $B$ para la función por partes $$Z(t) = \begin{cases} t^2 + At + 5, & 1 \leq t \leq 4 \\ B - t, & 4 < t \leq 10 \end{cases

1. **State the problem:** We have a piecewise function: $$f(x) = \begin{cases} -x^2 + 10 & \text{if } -4 \leq x < 4 \\ 6 - 3x & \text{if } x \geq 4 \end{cases}$$

1. **State the problem:** Solve the equation $$\frac{3}{x+1} - \frac{2}{x^2-1} = \frac{1}{x^2 - x}$$ for $x$. 2. **Identify the denominators and factor where possible:**

1. The problem states that the $r$th term of the first sequence is $2r^2 - 1$ and the $r$th term of the second sequence is $40 - r^2$. We need to show there is only one number comm

1. **State the problem:** We have two rectangles A and B. Rectangle A has dimensions $4x$ cm and $2.5$ cm.

1. **State the problem:** We have a trapezium ABCD with sides AD = $x$ cm, BC = $x$ cm, AB = $2x$ cm, and DC = $2x + 4$ cm. The perimeter is 38 cm. We need to find the length of AD

1. **Énoncé du problème :** Nous avons la fonction $g$ définie par $g(x) = x^3 - x^2 + 3x + 1$.