🧮 algebra

1. **State the problem:** Find the difference of squares from 2 to 20. 2. **Recall the difference of squares formula:**

1. **State the problem:** Simplify the expression $$\frac{C^2 - Cd}{d^2 - de} \div \frac{d^2 - Cd}{cd - ce}$$

1. **State the problem:** We are given an arithmetic progression (A.P) where the first term $A$ is equal to twice the common difference $d$. We need to find the fifth term of this

1. The problem states: If by decreasing $X$ by 10%, we get 180. We need to find the original value of $X$. 2. When a quantity is decreased by 10%, the new value is 90% of the origi

1. The first question to check is Question 4 (Simplifying Radicals). 2. The problem states: Simplify $\sqrt{128}$ and combine like terms.

1. **Problem statement:** We have two quadratic functions:

1. Planteamos el problema: Resolver la ecuación cuadrática $$3x^2 - 9x = 0$$. 2. Factorizamos la expresión para encontrar las soluciones. Sacamos factor común:

1. **State the problem:** We need to sketch the curve of the function $$f(x) = x^3 - 3x^2 + 2$$ and analyze its key features. 2. **Formula and rules:** To sketch a cubic function,

1. Écris chacune des expressions suivantes sous la forme logarithmique. Rappel : Pour une expression exponentielle $a^b = c$, la forme logarithmique est $b = \log_a c$.

1. **State the problem:** We are given the $n^\text{th}$ term of a sequence as $$a_n = \frac{2n}{5 - 9n}.$$ We need to find: a) The 10th term, $a_{10}$.

1. **State the problem:** We are given the $n^{th}$ term of a sequence as $$a_n = \frac{9 - 5n}{2n + 14}$$ We need to:

1. **State the problem:** Evaluate the expression $$\frac{-2 \times (3 - 4) + 5 \times (-1) + 2 \times 3 \times 4 - 17}{(\sqrt{2})^4 \times 3^2 - 2^3 \times 2^{-1} + 64^{1/3}}$$

1. **Problem:** Use the commutative property to show that the expressions are equal. 2. **Commutative Property of Multiplication:** This property states that for any numbers $a$ an

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{14.44} + \sqrt{9 + x^2} = 8.8.$$\n\n2. **Calculate the known square root:** \n$$\sqrt{14.44} = 3.8.$$\n\n3. **Rewrit

1. **State the problem:** We need to analyze the function $y = -|x^2 - 2|$ and find ordered pairs (points) on its graph. 2. **Understand the function:** The function involves the a

1. **Stating the problem:** Use the associative property of addition to show that the expressions are equal. 2. **Recall the associative property:** For any numbers $a$, $b$, and $

1. **Problem:** Use the associative property to show that the expressions are equal for (2 + 5) + 3. 2. **Formula:** The associative property of addition states that for any number

1. The problem is to understand the expression $|a-b|$ which represents the absolute value of the difference between $a$ and $b$. 2. The absolute value $|x|$ of a number $x$ is def

1. المشكلة: تحليل التعبير الجبري يعني تفكيكه إلى عوامل أبسط يمكن ضربها للحصول على التعبير الأصلي. 2. القاعدة الأساسية: لتحليل كثيرات الحدود، نبحث عن عوامل مشتركة أو نستخدم طرق مثل

1. The user asked for "other examples" but did not specify a particular math topic or problem. 2. To provide useful examples, I will give a few different types of algebra problems

1. Let's start by understanding what an "adequate example" means in math: it is a clear, simple instance that illustrates a concept or problem. 2. Example 1: Solve the linear equat