🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{xy + x^2y^2}{xy}.$$\n\n2. **Recall the rule:** When dividing a sum by a term, you can split the fraction as $$\frac{a+b}{c

1. The problem is to simplify the expression $\left(0.1 \times 10^{-3}\right)^{-2}$.\n\n2. Recall the rule for powers of a product: $\left(ab\right)^n = a^n b^n$. Also, the rule fo

1. **State the problem:** Simplify the expression $$\left(\frac{2}{5}\right)^{-2} \times 2^{-3}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $x^{-1} / x^{-2}$. 2. **Recall the rule for division of exponents with the same base:**

1. **State the problem:** Simplify the expression $$(5p^2)^2(2p)^2$$ and find which of the given options matches the simplified form. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{y^2 y^0}{y^{-2}}$$. 2. **Recall exponent rules:**

1. **State the problem:** Simplify the expression $3x - [(y - x) - (x - y)]$. 2. **Recall the rules:** When subtracting expressions inside brackets, distribute the minus sign to ea

1. **State the problem:** Simplify the expression $(2u - 3v - 1) - (u + 3v + u)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to e

1. The problem is to simplify the algebraic expression: $$2IR_1 - I_1R + 2I_1R + IR_1$$. 2. We use the distributive property and combine like terms. Terms with $IR_1$ and terms wit

1. Stating the problem: Solve the equation $$\frac{x + 1}{2} - 3 = \frac{2}{3}x - 1$$ for $x$. 2. Formula and rules: To solve linear equations, we isolate $x$ by performing inverse

1. **State the problem:** Solve the equation $$3x + 12 = 21$$ for $$x$$. 2. **Formula and rules:** To solve a linear equation like $$ax + b = c$$, isolate $$x$$ by performing inver

1. **Stating the problem:** Solve the quadratic equation $$-x^2 + 6x - 4 = 0$$ and find the turning point of the function $$f(x) = -x^2 + 6x - 4$$.

1. Planteamos el problema: Simplificar la expresión usando la propiedad distributiva. 2. La propiedad distributiva dice que $a(b+c) = ab + ac$.

1. Planteamos el problema: Dividir el polinomio $$P(x) = 5x^4 - 13x^3 + 2x - 1$$ entre el polinomio $$Q(x) = x^2 - 2x + 1$$. 2. Recordemos que para dividir polinomios usamos la div

1. **State the problem:** We need to find the percentage increase in the population of Ireland from 2016 to 2022. 2. **Given data:**

1. **State the problem:** We need to find the equation of the line $k$ that passes through the point $P(6, -3)$ and is perpendicular to the line $l$ given by the equation $$3x - 4y

1. The problem is to find the value of $V$ given the equations $\frac{U}{L} = T$, $L = \frac{T}{0}$, and $1 = \frac{V}{?}$. Also, we have $1 \times V = V = ?$. 2. First, note that

1. El problema demana resoldre les equacions de primer grau amb dues incògnites donades. 2. Les equacions són:

1. **State the problem:** Find the equation of the line $n$ passing through points $A(-1, 2)$ and $B(0, -2)$ in the form $y = mx + c$. 2. **Formula used:** The slope $m$ of a line

1. **State the problem:** Find the slope of the line passing through the points $(0,0)$ and $(3,2)$. 2. **Formula for slope:** The slope $m$ of a line passing through points $(x_1,

1. **State the problem:** Find the slope of the line passing through the points $(-6, -6)$ and $(0, -1)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ an