🧮 algebra

1. مسئله: مقدار $5/6$ برابر با $4/5$ چند است؟ 2. برای حل این مسئله، باید مقدار مجهول را $x$ در نظر بگیریم و معادله زیر را بنویسیم:

1. El problema es identificar si una expresión es un producto notable. 2. Los productos notables son expresiones algebraicas que se pueden factorizar o expandir fácilmente usando f

1. Énonçons le problème : on doit décomposer la fonction $$f(x,y) = x^2 y^2 + 2x^3 y^3 - x y^2 - x^2 y + x^2 y^3 + x^3 y^2$$. 2. La décomposition consiste à factoriser l'expression

1. Le problème : Comprendre la décomposition de Gauss et comment utiliser la formule $ (a+b)^2 $ dans ce contexte. 2. La formule importante : La décomposition de Gauss est une méth

1. **State the problem:** Solve the equation $2x = 64$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. Since $x$ is multipl

1. Planteamos el problema: Dada la ecuación ordinaria de la parábola $-1^2 = 2x + 2$, debemos hallar la ecuación general, el vértice, el foco y el lado recto. 2. Primero, interpret

1. Simplify $\frac{1}{\sqrt{3}+2}$ in the form $a+b\sqrt{3}$. Use rationalization: multiply numerator and denominator by the conjugate $2-\sqrt{3}$.

1. The problem is to expand and simplify the expression $ (y + 5)^2 $. 2. The formula for the square of a binomial is:

1. The problem is to simplify the expression $$\left(\frac{1}{2} + \frac{1}{x}\right)$$. 2. The formula to add fractions is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$.

1. The problem is to simplify the expression $4 - x^2$. 2. This is a difference of squares, which follows the formula $a^2 - b^2 = (a - b)(a + b)$.

1. The problem is to perform the division for the first expression in exercise 607: $$\frac{1}{3} : \frac{1}{9}$$. 2. Recall the rule for dividing fractions: dividing by a fraction

1. **State the problem:** Simplify the expression $$\frac{(\sqrt{5}-2\sqrt{6})(\sqrt{3}+\sqrt{2})}{\sqrt{3}-\sqrt{2}}$$. 2. **Recall the formula and rules:** To simplify expression

1. **State the problem:** Solve the inequality $$6(2x+1) - 8 > 5(1+2x) - 9$$. 2. **Apply the distributive property:**

1. We are asked to solve the inequality $$4(8 - x) \geq 3(3x - 20) - 25$$. 2. First, expand both sides using the distributive property:

1. **Stating the problem:** We have three sets of problems involving functions and points:

1. **State the problem:** Solve the inequality $3x^2 - x - 2 > 0$. 2. **Find the roots of the quadratic equation:** To understand where the parabola is above zero, first solve $3x^

1. نبدأ ببيان المسألة: لدينا دالة $m$ معرفة بالعلاقة $$m = w + (m - w) (f_1, f_2)$$ حيث $f_1 = 1$ و $f_2 = 0$. 2. نعلم أن $m$ يمكن كتابتها على شكل متعدد حدود من الدرجة الثانية: $$m

1. **State the problem:** Simplify the expression $$\frac{(2u^{2}v^{3}w^{3})(5u^{3}v^{4}w^{2})}{\frac{-2x^{3}y^{2}z}{6x^{2}y^{3}z^{6}}} \quad \text{and} \quad \frac{(3s^{11})(9s^{-

1. Stating the problem: Calculate the value of the expression $$56.403 + 0.000149(1724.4) - 0.0000593(63.51) + 0.163(35) + 0.873(0)$$. 2. Perform each multiplication:

1. **State the problem:** Find $x$ if $\log_3(2x + 5) = 5$. 2. **Recall the logarithm definition:** $\log_b(a) = c$ means $b^c = a$.

1. **State the problem:** Simplify and solve the equation $$\frac{3}{x+5} - \frac{1}{x^2 + 2x - 15} = \frac{1}{x+5}$$. 2. **Factor the quadratic denominator:** Note that $$x^2 + 2x