🧮 algebra

1. **Problem statement:** (a) Factorise completely the expression $x^3 - 4x$.

1. **State the problem:** Solve the quadratic equation $x^2 + 5 - 6 = 0$. 2. **Simplify the equation:** Combine like terms:

1. **بيان المسألة:** لدينا الدالة $$f(x) = \frac{2a - x^2}{x}$$ حيث $$a > 0$$ و $$x \neq 0$$. مطلوب حل البنود التالية: 2. **إيجاد معادلات خطوط التقارب المماسة للمحورين:**

1. **State the problem:** Solve the equation $$12 \left( \frac{x}{6} + 5 \right) = 5 \left( \frac{x}{5} - 30 \right)$$ for $x$. 2. **Use the distributive property:** Multiply insid

1. **State the problem:** Solve the quadratic equation $x^2 - 18x + 81 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **State the problem:** Simplify the expression $-32 - (-2 - 2 - 1)^2$. 2. **Understand the order of operations:** We first simplify inside the parentheses, then apply the expone

1. **Problem Statement:** Find all possible pairs $(a,b)$ such that the number $48a23b$ is a multiple of 18. 2. **Key Concept:** A number is a multiple of 18 if and only if it is d

1. Soal pertama: Sederhanakan ekspresi \( \frac{8a^{-3} b^5}{2a^6 b^2} \). 2. Gunakan aturan pangkat: \( \frac{a^m}{a^n} = a^{m-n} \) dan \( a^{-m} = \frac{1}{a^m} \).

1. **Problem statement:** The sum of three numbers is 174. The ratio of the second number to the third number is 9:16, and the ratio of the first number to the third number is 1:4.

1. **Problem Statement:** Given that $l^2 + m^2 + n^2 = 1$ and $l'^2 + m'^2 + n'^2 = 1$, find the value of $ll' + mm' + nn'$. 2. **Formula and Explanation:** The expressions $l^2 +

1. The first expression given is $2x - x^2 + 2xy - xy^2$. 2. The second expression to expand and simplify is $(x + a)(x + b) - (x - a)(x - b)$.

1. The problem is to calculate $5$ divided by $\frac{11}{2}$. 2. The formula for dividing by a fraction is to multiply by its reciprocal: $a \div \frac{b}{c} = a \times \frac{c}{b}

1. The problem asks us to graph a line with a slope of 7 that passes through the point (0, 3). 2. The formula for a line in slope-intercept form is $$y = mx + b$$ where $m$ is the

1. مسئله را بیان می کنیم: شما می خواهید یک مسئله ریاضی را با راه حل ساده و قابل فهم برای دانش آموز کلاس ششم داشته باشید. 2. فرض کنیم مسئله این است: حل معادله ساده $2x + 3 = 11$.

1. **State the problem:** A sum of 7200 is divided between A and B in the ratio 5:4. We need to find how much B gets. 2. **Formula and explanation:** When a total amount is divided

1. **State the problem:** Find the least common multiple (LCM) of 24 and 36. 2. **Recall the formula:** The LCM of two numbers $a$ and $b$ can be found using the formula:

1. The problem is to convert the decimal number 0.625 into a fraction. 2. To convert a decimal to a fraction, write the decimal as a fraction with denominator as a power of 10 base

1. **State the problem:** We are given the ratio of girls to boys as 3:5 and the total number of students is 40. We need to find how many are girls. 2. **Formula and explanation:**

1. The problem is to find the missing number in the bottom pie chart segment marked with a question mark (?). 2. We observe that the top two pie charts have segments:

1. The problem asks us to identify which number is irrational. 2. An irrational number is a number that cannot be expressed as a fraction $\frac{a}{b}$ where $a$ and $b$ are intege

1. **State the problem:** Solve the system of equations using the Gauss-Jordan method: $$\begin{cases} 2x + y - z = 8 \\ -3x - y + 2z = -11 \\ -2x + y + 2z = -3 \end{cases}$$