🧮 algebra

1. **State the problem:** Factor the expression $$16x^2y^8 - 4$$. 2. **Identify common factors:** Both terms have a common factor of 4.

1. **State the problem:** Given the equation $x^2 + y^2 = 1$, show that $$\frac{\frac{x}{y}}{1 + \frac{y^2}{x^2}} = xy.$$\n\n2. **Rewrite the expression:** The left side is a compl

1. The problem asks to simplify the expression $$\frac{x}{y}$$ given the context of question 23. 2. Since the user message includes multiple expressions but requests to solve quest

1. The problem is to solve the equation shown in the screenshot (assuming it is a quadratic equation or similar). Since the image is not accessible, please provide the equation tex

1. The problem asks to solve parts a and d of a given question, but since the exact question is not provided, I will demonstrate how to solve a typical algebraic problem for part a

1. **Problem Statement:** Martina's pension contributions follow a ratio of 3:3:1 for employee, employer, and State respectively, totaling €1351 in the first year. We need to find

1. **Problem:** Write an equation in slope-intercept form of the line that passes through the point (1, 3) and is parallel to the graph of the equation $y = 3x + 2$. 2. **Recall:**

1. **State the problem:** Eleven's garden is rectangular with an area of 240 square feet. The length and width are consecutive even numbers. We need to find the perimeter of the ga

1. Plantegem el problema: Resoldre el sistema lineal per el mètode de Gauss: $$\begin{cases} x + 2y - z = 0 \\ 2x - y + z = -1 \\ -x + y + z = 6 \end{cases}$$

1. **State the problem:** Find the value of $x$ when the area of the rectangle is 10 cm². 2. **Formula for area of a rectangle:**

1. **State the problem:** Simplify the expression $2(3a+4b)-(8a-b)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Simplify the expression $$2(3a + 4b) - (8a - b)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside

1. **Problem:** Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. 2. **Recall:** Lines t

1. State the problem: Prove that $$\left\lfloor\frac{x+2}{2}\right\rfloor-2\left\lfloor\frac{x+2}{4}\right\rfloor = 1-\left(\left\lfloor\frac{x}{2}\right\rfloor-2\left\lfloor\frac{

1. The problem is to find 5% of 16. 2. The formula to find a percentage of a number is:

1. **State the problem:** Nadia earns a weekly allowance of $400 plus 5% commission on her sales. We want to find:

1. **Problem:** Simplify the expression $1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \frac{1}{32}$. 2. **Formula and rules:** This is a finite geometric series wit

1. **State the problem:** Simplify the expression $$\frac{18 - x}{3x - 1} \times \frac{7 - 21x}{2x - 36}$$. 2. **Rewrite each part by factoring where possible:**

1. Il problema chiede se $x = -2$ è soluzione di $x^2 - 4 = 0$ o di $x^2 + 4 = 0$. Verifichiamo sostituendo $x = -2$ in entrambe le equazioni. 2. Per $x^2 - 4 = 0$, sostituiamo:

1. The problem is to identify the slope and y-intercept of the line given by the equation $y = -2x + 11$. 2. The equation is in slope-intercept form $y = mx + b$, where $m$ is the

1. Let's clarify the problem: You asked "where did you get the 3?" which suggests you want to understand the origin of the number 3 in a previous math step. 2. Typically, the numbe