🧮 algebra

1. **Problem statement:** Simplify the expressions: (i) $ (4\sqrt{3} - 2\sqrt{2})(3\sqrt{2} + 4\sqrt{3}) $

1. **Problem statement:** Find the maximum and minimum values of the function $$f(x) = \frac{2x^2 + 4x + 5}{x^2 + 1}$$ for all real numbers $x \in \mathbb{R}$. 2. **Formula and rul

1. **State the problem:** Solve the inequality $$9x^2 + 3x - 2 \geq 0$$ and graph the solution set on a real number line. 2. **Formula and rules:** To solve a quadratic inequality,

1. **State the problem:** Evaluate the determinant of the matrix $$D = \begin{vmatrix} 1 & 2 & -1 \\ 3 & 0 & 0 \\ 2 & -2 & -1 \end{vmatrix}$$

1. **State the problem:** Find the value of $$k^2 + \frac{1}{k^2}$$ where $$k = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$$.

1. **Problem:** Simplify the expression $$11\sqrt[3]{x^4 y^7} - 5xy \sqrt[3]{8xy^4} + y^2 \sqrt[3]{27x^4 y}$$ and verify it equals $$4xy^2 \sqrt[3]{xy}$$. 2. **Formula and rules:**

1. **Stating the problem:** We are given several expressions involving variables $x$, $u$, and $u_1$, and we want to understand and solve for $u$ and $u_1$ based on the given equat

1. **Problem:** Mahi, Lara, and Maivi participated in a quiz contest. Mahi and Lara scored 45 and 18 points respectively. Find how many points Maivi scored. 2. **Write an equation:

1. **Stating the problem:** We want to find the equation of the curve outlining the trophy shape, which is given as a parabola segment $$y = -(0.16x - 2.109)^2 + 4.28$$ for $$1.963

1. **Stating the problem:** We are given several algebraic expressions and equations to build up and undo, and to solve for variables. 2. **Building and undoing expressions:**

1. The problem asks to find the geometric means of the sequence: 0.5, ____, ____, ____, 2048. 2. The geometric means are the terms between the first and last term in a geometric se

1. The problem asks to find the sixth term of the expansion of $ (c + d)^{10} $. 2. The general term in the binomial expansion of $ (a + b)^n $ is given by:

1. Problem statement: Diana wants to buy three equally priced pants for a total of 84 euros. She has 140 euros in cash. 2. Find the price of one pant by dividing the total cost by

1. **Problem statement:** Helmut earns 25 euros for 2.5 hours of work. We want to find out how much he earns after 12 hours. 2. **Formula and rule:** Since the pay is proportional

1. **State the problem:** Simplify the fraction $\frac{2444}{27}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common divis

1. **State the problem:** Solve the linear equation $5x - 10 = 2x + 20$ for $x$. 2. **Write down the formula and rules:** To solve for $x$, we need to isolate $x$ on one side of th

1. **State the problem:** Simplify the expression $$(2x^2 - 2x - 12)(3x^2 - 10x + 3).$$ 2. **Factor each polynomial:**

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 2x - 12}{3x^2 - 10x + 3}$$ and determine which of the given options matches the simplified form. 2. **Factor numera

1. **State the problem:** Calculate the sum and difference of the fractions $\frac{14}{27} + \frac{5}{27} - \frac{16}{27}$ and simplify the result. 2. **Formula and rules:** When a

1. **Stel het probleem vast:** We hebben punten $A(k,1)$ en $B(-1,2)$ en een rechte $r: 2x - 3y - 2 = 0$.

1. **State the problem:** We have three equations involving three items: red apple (A), banana bunch (B), and coconut half (C). The equations are: $$A + B + B = 18$$