🧮 algebra

1. Énoncé du problème : Calculer $$\frac{(2a+3b)^2-(2a-3b)^2}{4b}$$ et expliquer les étapes. 2. Utiliser l'identité remarquable de la différence de carrés : $$x^2 - y^2 = (x-y)(x+y

1. The problem is to "Add another 7 to the bottom" which likely means to add 7 to the denominator of a fraction or an expression. 2. Suppose we have a fraction $\frac{a}{b}$ and we

1. State the problem: Simplify the expression $$\frac{7}{\frac{7}{7}}$$. 2. Simplify the denominator: The denominator is $$\frac{7}{7}$$, which equals $$1$$ because $$7 \div 7 = 1$

1. Let's first clarify the problem: "It’s have to be 49." If this means we need to find a number or expression that equals 49, we can start by considering simple squares since 49 i

1. **State the problem:** Simplify the expression $\frac{7}{\frac{7}{7}}$. 2. **Simplify the denominator:** Calculate $\frac{7}{7}$. Since 7 divided by 7 is 1, this simplifies to 1

1. **State the problem:** Solve the equation $$\frac{3x + 2}{x - 1} = 2\sqrt{x + 3} - 1$$ for $x$.

1. Stated problem: Solve the quadratic equation $3x^2 - 110x + 60 = 0$. 2. Identify coefficients: $a = 3$, $b = -110$, $c = 60$.

1. Problem: Simplify the expression $$\frac{x^2 - y^2}{x + y}$$. 2. Recognize that the numerator is a difference of squares: $$x^2 - y^2 = (x - y)(x + y)$$.

1. State the problem: Simplify the expression $$ A = \frac{12}{8} - \frac{6}{8} \div \frac{5}{4} $$.\n\n2. Simplify the first fraction: $$ \frac{12}{8} = \frac{3}{2} $$.\n\n3. Perf

1. We are given the system of inequalities: $$3x + y \geq 15$$

1. Evaluate the following complex number operations: i) \((2 + 3i) + (7 - 2i)\)

1. The problem asks us to simplify the expression $(x-120)^2$. 2. Recall that $(a-b)^2$ expands using the formula: $$ (a-b)^2 = a^2 - 2ab + b^2 $$

1. **State the problem:** We need to solve the system of inequalities graphically and determine if the solution region is bounded or unbounded. The system is: $$3x + y \geq 15$$

1. The user requested to create the picture for the graph of the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. This is an exponential function which is important in algebra f

1. **State the problem:** Find the solution region for the system of inequalities:

1. سنبدأ بحساب أولية العدد 756. 2. أولاً، نحدد إذا كان العدد 756 يقبل القسمة على الأعداد الأولية الصغيرة مثل 2 و 3 و 5.

1. The problem is to simplify and evaluate the expression $$(2^2 \cdot 3^3 \cdot 7)^2$$. 2. First, simplify inside the parentheses by calculating each power:

1. لنقم بتحديد ما إذا كان 27 عددًا أوليًا أم لا. 2. العدد الأولي هو العدد الذي له عاملان فقط: 1 ونفسه.

1. Problem statement: Evaluate the expression $\sqrt{7}-\sqrt{2}\{2\}$. 2. Interpretation: We interpret $\{2\}$ as the fractional part of 2, defined by $\{x\}=x-\lfloor x\rfloor$.

1. **Stating the problem:** We analyze the function $$f(x) = \frac{x}{2x^{2} - 3x + 1} + \sqrt{\frac{x-1}{1-2x}}$$

1. **State the problem:** Simplify $$4 + i^5$$ and $$2i^{13} - (i^{41} + i)$$ where $$i$$ is the imaginary unit with property $$i^2 = -1$$. 2. **Recall powers of $$i$$:**