🧮 algebra

1. **State the problem:** Solve the equation $n^2 = 4(4n + 9)$. 2. **Write the equation and expand:** Start with the given equation:

1. **State the problem:** Solve the equation $$y^2 + 2y - x^2 + 6y = -10x$$ for $y$ in terms of $x$. 2. **Combine like terms:** Group the $y$ terms together:

1. **State the problem:** We need to understand and graph the function $f(x) = -4^x$. 2. **Recall the function form:** The function is an exponential function with base 4 and a neg

1. The problem is to draw the graph of the function $f(x) = -4x$. 2. This is a linear function of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. **Énoncé du problème :** Résoudre l'inéquation $$\frac{2x^{2} - 5x + 3}{3x - 1} \geq 0.$$ 2. **Formule et règles importantes :**

1. El problema es demostrar que $\sqrt[n]{a^m} = a^{\frac{m}{n}}$. 2. La fórmula para convertir una raíz en una potencia es:

1. The problem involves two expressions: $x - 8$ and $y - 6$. 2. These expressions represent values shifted from $x$ and $y$ by 8 and 6 units respectively.

1. **State the problem:** Simplify the quadratic expression $6x^2 - 30x + 24$ by factoring. 2. **Formula and rules:** To factor a quadratic expression, first find the greatest comm

1. **State the problem:** Simplify or factor the quadratic expression $6x^2 - 30x + 24$. 2. **Identify the greatest common factor (GCF):** The coefficients 6, -30, and 24 share a G

1. مسئله: جمع دو عبارت جبری $\left(x^3 + 7x^3y^3 + 16xy + 5\right)$ و $\left(3x^3 - 1.2x^3y^3 - 8xy\right)$ را بیابید. 2. قانون: برای جمع عبارات جبری، ضریب‌های جملات هم‌نوع (یعنی ج

1. Problema: Simplificar la expresión $$\left(\frac{X^{3/2}}{X^{1/2}}\right)^2$$. Usamos la ley de los exponentes para división: $$\frac{a^m}{a^n} = a^{m-n}$$.

1. **State the problem:** Write $$\frac{3}{x+4} + \frac{5}{x^2 - 16}$$ as a single fraction in simplest form. 2. **Identify the denominators:** The denominators are $$x+4$$ and $$x

1. Stating the problem: Simplify the expression $$\left(\frac{29 - 1}{b - 1}\right)^{-2} : \left(\frac{49 - 2}{b - 3}\right)^{-1}$$. 2. Simplify the numerators inside the parenthes

1. The problem is to simplify the expression or solve the equation in one calculation line. 2. To do this, we use algebraic rules such as combining like terms, applying distributiv

1. **State the problem:** Solve the linear equation $$\frac{1}{3}x - \frac{3}{4} = \frac{1}{2}x - \frac{2}{3}$$ for $x$. 2. **Write down the equation:**

1. **Problema:** Dados $a+b=4$ y $ab=6$, calcular $A=\sqrt{a^2+b^2}$. 2. **Fórmula y reglas:** Sabemos que $a^2+b^2=(a+b)^2-2ab$.

1. The problem asks to describe the end behavior of a polynomial function $P$ which is the sum of two polynomials: one of degree 2 with a positive leading coefficient, and one of d

1. Enunciem el problema: Factoritzar el polinomi $$3x^4 + 3x^3 - 21x^2 - 3x + 18$$. 2. Primer, busquem un factor comú en tots els termes. Observem que tots els coeficients són múlt

1. **State the problem:** Simplify the expression $$\frac{x-1}{x-2} - \frac{x-2}{x+2}$$. 2. **Formula and rules:** To subtract fractions, find a common denominator and combine the

1. **State the problem:** Simplify the square root of 674, i.e., find $\sqrt{674}$ in simplest radical form. 2. **Recall the formula and rules:** To simplify $\sqrt{n}$, find the l

1. **State the problem:** Simplify the given fractions: $$\frac{x + 1}{4x + 4}, \quad \frac{4x - 32}{x^2 - 5x - 24}, \quad \frac{x - 3}{5x - 15}, \quad \frac{x^2 + 3x - 18}{x^2 + 1