🧮 algebra

1. **State the problem:** Simplify the expression $2a\sqrt{3} - \sqrt{27a^2} + a\sqrt{12}$. 2. **Recall the rules:**

1. **Problem:** Find the equation of a straight line with gradient $m$ passing through a point $(x_1, y_1)$. 2. **Formula:** The point-slope form of a line is given by:

1. **Problem:** Factor the polynomial $4x^2 - 1$ using a special pattern. 2. **Formula and rules:** This is a difference of squares pattern: $$a^2 - b^2 = (a - b)(a + b)$$ where $a

1. **State the problem:** Simplify the expression $$\sqrt[3]{512x^4 y^5}$$. 2. **Recall the cube root properties:** The cube root of a product is the product of the cube roots: $$\

1. **State the problem:** Simplify the expression $$(4 \times \sqrt{18x}) (6 \sqrt{6x})$$. 2. **Recall the properties of square roots and multiplication:**

1. The problem appears to involve understanding the relationship between the numbers given: $4 = 24$, $- 6 = 4$, and $= 4 \times 6$. We need to clarify what is being asked, but sin

1. **State the problem:** Simplify the expression $\frac{y}{12x^5} + \frac{5}{9x^2}$. 2. **Find a common denominator:** The denominators are $12x^5$ and $9x^2$. The least common de

1. **Problem Statement:** Simplify the complex rational expression. For example, simplify $$\frac{\frac{a}{b} + \frac{c}{d}}{\frac{e}{f} - \frac{g}{h}}$$. 2. **Formula and Rules:**

1. Stating the problem: Simplify the expression $3(m+n)^2$. 2. Recall the formula for the square of a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$

1. **State the problem:** Simplify the expression $$\frac{e^3 - \ln(4)}{3 + e \sqrt{e + 1 + \pi}} - 4e$$. 2. **Recall the components:**

1. El problema pide realizar el producto entre monomios. Vamos a resolver el inciso a) que es el primer problema. 2. El producto entre monomios se realiza multiplicando los coefici

1. The problem is to convert a fraction or expression into a decimal answer. 2. To convert a fraction to a decimal, divide the numerator by the denominator.

1. **State the problem:** Solve the quadratic equation $$5r^2 + r - 2 = 0$$ for all real values of $r$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$,

1. **State the problem:** Find the least common denominator (LCD) for each pair of rational expressions given. 2. **Recall the rule:** The LCD of rational expressions is the least

1. **State the problem:** Solve the inequality $2(x+3)<14$ for $x$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses.

1. Planteamos el problema: Resolver la ecuación logarítmica $\log(3x+5)=2$. 2. Recordemos que $\log_b(a)=c$ significa que $b^c=a$. Aquí, el logaritmo es base 10 (logaritmo común),

1. **State the problem:** Solve the equation $2(4x+3)+4=-2(-4x-6)-2$ using the river method. 2. **Distribute the constants:**

1. **State the problem:** Simplify the expression $\frac{3x - 2}{4}$. 2. **Understand the expression:** The expression is a fraction with numerator $3x - 2$ and denominator $4$.

1. **State the problem:** Solve the equation $2(4x+3)+4=-2(-4x-6)-2$ for $x$. 2. **Apply the distributive property:** Multiply out the parentheses.

1. **State the problem:** Solve the inequality $$\frac{|3x - 4|}{2} \geq \left|\frac{5}{12}\right|$$. 2. **Recall the properties:** The absolute value is always non-negative, and $

1. Stwierdźmy problem: Rozwiąż nierówność $$\frac{3x - 2}{\frac{x}{4}} \geq -1$$. 2. Przekształćmy wyrażenie w liczniku i mianowniku, aby uprościć nierówność. Zauważmy, że dzieleni