🧮 algebra

1. Énoncé du problème : Développer et réduire l'expression $$ (\sqrt{3} + 2)^2 $$. 2. Commencer par appliquer la formule de développement du carré d'une somme : $$ (a + b)^2 = a^2

1. Énoncé du problème : Calculer $\left(3\sqrt{11} + 3\right)\left(2\sqrt{11} + 2\right)$ et donner la réponse sous la forme $a + b\sqrt{c}$ où $a,b$ sont des nombres entiers ou fr

1. Stating the problem: Calculate the result of the division $+16 \div +8$. 2. Division of two positive numbers: When dividing two positive numbers, the result is also positive.

1. Énonçons le problème : Simplifier l'expression $$3\sqrt{5} \times (-4)\sqrt{8}$$ en une forme du type $$a\sqrt{b}$$ ou un entier/fraction si possible. 2. Réécrivons l'expression

1. Énonçons le problème : calculer $$2\sqrt{275} + 2\sqrt{44} + \sqrt{891}$$ et simplifier l'expression. 2. Factorisons les radicaux pour extraire les carrés parfaits.

1. **State the problem:** Solve the system of linear equations: $$2x + y - z + 3t = 5$$

1. The problem is to simplify the expression $(-15) \times \left(+ \frac{3}{5}\right)$.\n2. First, multiply the numbers ignoring the sign: $15 \times \frac{3}{5} = \frac{15 \times

1. We are asked to simplify and evaluate the expression $$4^{2020} + 2^{2017} - 15.$$\n\n2. Notice that $$4^{2020} = (2^2)^{2020} = 2^{4040}.$$\n\n3. So the expression becomes $$2^

Problem: Solve for $x$ given $x^{-1/3} = y$. 1. Observe the expression and rewrite the power in root form to understand it better.

1. We are asked to find the minimum integer value of the function $$y = 2^{3x+5} - 1$$. 2. The function is an exponential function with base 2, which is always positive.

1. We start by stating the problem: prove that for any real numbers $x$ and $y$, the inequality $$|x| + |y| < |x+y| + |x-y|$$ holds. 2. Recall the triangle inequality: for all real

1. State the problem: Solve the inequality $$2^{x-1} \geq 8$$. 2. Express 8 as a power of 2: Since $$8 = 2^3$$, rewrite the inequality as $$2^{x-1} \geq 2^3$$.

1. The problem asks us to find the sum of the roots of the quadratic equation $$3x^2 + 14x - 5 = 0$$. 2. Recall that for a quadratic equation $$ax^2 + bx + c = 0$$, the sum of the

1. The problem is to find the domain of the function $$y = \log_4 (1 - x)^7$$.\n\n2. Recall that the domain of a logarithmic function $$\log_a b$$ requires the argument $$b$$ to be

1. The problem asks us to find the amount in excess of 12000. 2. To solve this, subtract 12000 from the total amount given or found.

1. **State the problem:** Mr Simba's salary is 35000 per month and his wife's salary is 23000 per month. We want to find the total income tax they pay in one year given the tax rat

1. **State the problem:** Mr Simba's monthly salary is 35000 and his wife's monthly salary is 23000. We need to find the total income tax they pay in one year based on the tax rate

1. We start with the initial value of the car, which is $1000000$. 2. The value of the car depreciates by $5\%$ every year, so the value at the end of each year can be calculated a

1. Énonçons le problème : calculer et simplifier l'expression $10\sqrt{7} + 9\sqrt{15} + 10\sqrt{7} + 9\sqrt{15}$. 2. Regroupons les termes semblables :

1. Le problème est de développer et réduire l'expression $$(\sqrt{3} - 2)(\sqrt{3} - 2).$$ 2. On applique la formule de développement pour le produit de deux binômes identiques : $

1. مسئله را شرح می‌دهیم: دنباله $$5-10+15-20+25-30+\cdots+95-100$$ را می‌خواهیم حل کنیم. 2. این دنباله شامل جملات زوج است که به صورت مثبت و منفی به ترتیب تکرار می‌شوند.