🧮 algebra

1. **State the problem:** Multiply the two polynomials $$(x^2 + 2x - 1)(x^2 - x - 4)$$. 2. **Recall the distributive property:** To multiply two polynomials, multiply each term in

1. **State the problem:** Simplify the expression $2 - (3x + 2)$. 2. **Recall the rule:** When subtracting a quantity in parentheses, distribute the minus sign to each term inside.

1. **State the problem:** We need to find how many azzes are in 1 enit given the conversion rates between different coins. 2. **Given conversions:**

1. The problem asks us to compare $12.5 \times 10^{-4}$ and $1.25 \times 10^{-3}$. 2. Both numbers are in scientific notation, which is expressed as $a \times 10^n$ where $a$ is th

1. **State the problem:** Solve the equation $$2(x - 5) + 8x = 20$$ for $x$. 2. **Apply the Distributive Property:** Multiply 2 by each term inside the parentheses:

1. **State the problem:** Solve the equation $2(x - 5) + 8x = 20$ for $x$. 2. **Apply the Distributive Property:** Multiply $2$ by each term inside the parentheses.

1. **State the problem:** Simplify the expression $$\frac{a^{2/3}}{b^{1/3}} + \frac{b^{2/3}}{a^{1/3}}$$ and find which given option it is equivalent to. 2. **Rewrite the expression

1. **Stating the problem:** Simplify the expression $x(12y^2 + 16)x(12y^2 + 16)x(12y^2 + 16)$. 2. **Rewrite the expression:** Notice that the expression is $x(12y^2 + 16)$ multipli

1. **State the problem:** Solve and graph the system of linear equations: $$\begin{cases} X + Y = 2 \\ X - Y = 4 \end{cases}$$

1. The problem is to evaluate the expression $2000(1.10)^{0.5}$. 2. The expression involves multiplying 2000 by the square root of 1.10, since raising to the power 0.5 is equivalen

1. **Stating the problem:** You asked to fill in the JSON response with all the information you gave, which is a request to demonstrate the format and content structure for a math

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} X + Y = 2 \\ X - Y = 4 \end{cases}$$

1. The problem asks to express two equations in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 2. The general form $y = mx + b$ means the equation is sol

1. **State the problem:** We need to choose the correct system of equations where $x$ is the number of Christmas ornaments and $y$ is the number of doll dresses, then solve the sys

1. **State the problem:** We want to subtract the fractions $\frac{5}{x}$ and $\frac{2x + 10}{x}$.\n\n2. **Look at the denominators:** Both fractions have the same denominator $x$,

1. **State the problem:** Simplify the expression $$\frac{5}{x} - \frac{2x + 10}{x}$$. 2. **Identify the common denominator:** Both terms have the denominator $x$, so we can combin

1. **State the problem:** We are given a relation M with points $(x, y)$ as follows: $(-1, 3)$, $(0, 6)$, $(2, 12)$, and $(3, 15)$. We need to determine the nature of the rate of c

1. **Problem:** Determine which pair of points shows a graph that is not a function. 2. **Recall the definition of a function:** A graph represents a function if every input (x-val

1. **Problem statement:** Three fifths of those present agreed, and the remaining 12 disagreed. Find: a. The fraction of those who disagreed.

1. **State the problem:** We have the function $$f(x) = \frac{\lfloor x \rfloor + x}{2}$$ where $$\lfloor x \rfloor$$ is the greatest integer less than or equal to $$x$$. We want t

1. **State the problem:** Simplify the expression $$\frac{x^4 + 8x^3 + 24x^2 + 32x + 16}{x^3 + 6x^2 + 12x + 8}$$ and determine its domain. 2. **Recognize the polynomials:** Both nu