🧮 algebra

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

1. **State the problem:** Calculate the value of $\left(\frac{\sqrt{3}}{2}\right)^2$. 2. **Formula used:** When squaring a fraction, square the numerator and the denominator separa

1. The problem is to analyze the system of inequalities: $$y \leq x + 10$$

1. **State the problem:** Solve the inequality $$\frac{|3 - 2x|}{1 + x} < 4$$. 2. **Understand the components:** The numerator is an absolute value expression, which means it is al

1. **Problem:** Find the highest common factor (HCF) of $12x^{12}$ and $16x^{16}$. 2. **Formula and rules:**

1. Find the highest common factor (HCF) of $12x^{12}$ and $16x^{16}$. The HCF of two terms is found by taking the HCF of the coefficients and the lowest power of common variables.

1. **Problem 474:** Simplify $$2(m - n)^2 (m + n) - 2(m + n)^2 (n - m) - 4m(m - n)(m + n)$$ 2. **Step 1:** Expand and rewrite terms.

1. **State the problem:** We are given two cubic polynomial functions: $$P(x) = \frac{3}{2}x^3 + 2x^2 + \frac{1}{2}x + 1$$