🧮 algebra

1. **Énoncé du problème :** Factoriser les expressions suivantes : $$A = n^{12} - 2n^6 + 1$$

1. Soal: Tentukan himpunan penyelesaian dari persamaan $2x + 3y = 6$. 2. Gunakan rumus persamaan garis lurus $Ax + By = C$.

1. Masalah: Morgan ingin membuat topi (A) dan terompet (B) dengan anggaran 1000. Biaya topi Rp 25 per unit dan terompet Rp 50 per unit.

1. The problem is to perform math operations as if writing on homework paper. 2. Since no specific math problem is given, I will demonstrate a simple algebraic example: Solve for $

1. نبدأ بكتابة التعبير المطلوب تبسيطه: $$\frac{3}{\sqrt{3}-2}$$

1. **Problem:** Find the slope of the function $P = 12 - Q$ at all values of $Q$. 2. **Formula:** The slope of a function is given by its derivative with respect to the independent

1. مسئله: تعداد ارقام عدد حاصل از ضرب $$40^{18} \times 250^{10}$$ را بیابید. 2. برای یافتن تعداد ارقام یک عدد مثبت $N$، از رابطه استفاده می‌کنیم:

1. **Problem statement:** (a) Chamod's annual income from properties is 200000 rupees. He earns 60000 rupees per month from his job.

1. **Problem statement:** We have the sequence defined by $$u_n = \frac{1}{n+1} + \frac{1}{n+2} + \cdots + \frac{1}{2n}$$ for all $n \geq 1$. We want to show that $$\frac{1}{2} \le

1. **State the problem:** Find the vertex of the quadratic function $g(x) = x^2 - 4x + 7$ and determine its properties. 2. **Formula and rules:** For a quadratic function $ax^2 + b

1. **State the problem:** We are given the function $g(x) = x^2 - 4x + 7$ and want to analyze its properties, including finding the vertex and understanding the shape of its graph.

1. The problem involves understanding the equations $x = y + z$ and $f(x) = a^2 + b^2 = c^2$. 2. The first equation $x = y + z$ is a simple linear relation where $x$ is the sum of

1. **State the problem:** We need to find the cost of one iPhone given the total costs of purchases made by James and Peter. 2. **Define variables:** Let $x$ be the cost of one iPh

1. **State the problem:** Solve the equation $9j + 3 = 3(3j + 1)$. 2. **Write the formula and rules:** Use the distributive property to expand the right side: $a(b + c) = ab + ac$.

1. The problem asks us to find a solution to the given equation. However, the equation itself is not provided in the message. 2. To solve an equation, we typically isolate the vari

1. **State the problem:** Solve the quadratic equation $w^2 + 12 - 40 = 0$. 2. **Rewrite the equation:** Simplify the constant terms:

1. **Énoncé du problème :** On considère la suite $(u_m)$ définie par $u_0=1$ et $u_{m+1} = \frac{3u_m + 2}{u_m + 2}$ pour tout $m \in \mathbb{N}$. 2. **Montrer que $1 < u_m < 2$ p

1. **State the problem:** Akosua bought 5 loaves of bread and 3 sachets of margarine for a total of 8.

1. The problem is to simplify the expression $9^{\frac{3}{2}}$. 2. Recall the rule for fractional exponents: $a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$.

1. **Problem statement:** An article is sold by X to Y at a loss of 20%, Y to Z at a gain of 15%, Z to W at a loss of 5%, and W to V at a profit of 10%. V pays 500. We need to find

1. The problem is to determine whether two given pairs (usually pairs of algebraic structures, graphs, or sets with operations) are isomorphic or not. 2. Two pairs are isomorphic i