🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{a^5 y^3}{w y^2} \div \frac{a^3 w^2}{w^3 y^2}.$$ 2. **Rewrite the division as multiplication by the reciprocal:**

1. El problema es encontrar la función y describir su gráfica para la función dada $f(x) = x^2$. 2. La fórmula es $f(x) = x^2$, que representa una parábola con vértice en el origen

1. **State the problem:** Simplify the expression $4(a+4b)-2(a+b)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. The problem is to simplify the expressions $x-4$ and $x-6$ or to understand their difference. 2. These are linear expressions representing values decreased by 4 and 6 respective

1. **State the problem:** Perform the long division of the polynomial $$x^8 - 4x^7 + 6x^5 - 2x^4 + 3x^2 + 4$$ by the divisor $$x^3 + 2$$. 2. **Recall the long division formula:** W

1. El problema es realizar la división larga de polinomios y completar los polinomios faltantes. 2. La división larga de polinomios se realiza similar a la división larga de número

1. Het probleem is om de waarde van $\sqrt{4:25}$ te vinden. 2. Eerst interpreteren we de notatie: $4:25$ betekent $\frac{4}{25}$.

1. **State the problem:** We need to identify the graph of the quadratic function $$y = 12x^2 - 80x + 270$$. 2. **Recall the properties of quadratic functions:** The graph of a qua

1. Stating the problem: Simplify the expression $$\frac{3\sqrt{42}}{2\sqrt{6}} - \frac{\sqrt{35}}{\sqrt{5}}$$. 2. Simplify each term separately.

1. **State the problem:** We need to complete the table of values for the function $$f(x) = \frac{4}{x-2}$$ at the points $$x = -2, -1, 0, 1, 2, 3, 4$$. 2. **Recall the function an

1. Planteamos el problema: Pedro divide su terreno en dos partes, llamémoslas $x$ y $y$, con $x + y = 11600$ m². 2. Según el enunciado, $\frac{2}{5}$ de la primera parte mide lo mi

1. **Problem Statement:** Learn how to work with exponents, including evaluating expressions with positive and negative exponents, simplifying expressions with exponents, and apply

1. **State the problem:** Solve the equation $$x^4 - 5x^2 + 4 = 0$$ for $x$. 2. **Use substitution:** Let $y = x^2$. Then the equation becomes a quadratic in $y$:

1. **Сформулюємо першу систему рівнянь:** $$\begin{cases} x + y = 5 \\ y^2 + 4xy = 33 \end{cases}$$

1. **State the problem:** Find the non-zero values of $a$ and $b$ such that $$(2x - a)^3 = 8x^3 - bx^2 + \frac{3}{2} b x - a^3.$$

1. **State the problem:** Find the non-zero values of $a$ and $b$ such that $$(2x - a)^3 = 8x^3 - bx^2 + 2bx - a^3.$$ 2. **Recall the binomial expansion formula:** For any $u$ and

1. **Problem:** Simplify the expression $$\frac{\frac{3y^2 + 9x^2 - 7a - 9}{7x - 9}}{\frac{x^2 - 3x + 11}{3x - 9 - 11}}$$. 2. **Formula and rules:** When dividing fractions, multip

1. **State the problem:** Solve the system of inequalities: $$\frac{x-2}{x-4} < 0$$

1. **State the problem:** Find all real solutions to the equations: (i) $$16a^2 = 2\sqrt{a}$$

1. The problem states that the roots of the cubic equation $$x^3 - 2x^2 + 4x - 5 = 0$$ are $$p$$, $$q$$, and $$r$$. We need to find the value of $$(p - 4)(q - 4)(r - 4)$$ without s

1. **State the problem:** We need to determine which expressions always yield an even value when $x$ is an odd number. 2. **Recall important rules:**