🧮 algebra

1. **State the problem:** Simplify the expression $6x^2y + 5xy^2 - x^2y + 3xy^2$. 2. **Group like terms:** Group terms with $x^2y$ and terms with $xy^2$ separately:

1. **State the problem:** We have four quadratic functions: $y = A x^2$, $y = B x^2$, $y = C x^2$, and $y = D x^2$. (a) Determine the sign (positive or negative) of each coefficien

1. The problem is to solve the equation given by the user, but since no specific equation was provided, let's consider a general example: Solve for $x$ in the equation $2x + 3 = 7$

1. **Problem:** Simplify the expression \((5rt - 3rw - 8tw) + (6rt - 4rw + 2tw)\). 2. **Formula and rules:** To add polynomials, combine like terms. Like terms have the same variab

1. **State the problem:** Simplify or factor the cubic polynomial $x^3 + 2x^2 - 5x - 6$. 2. **Formula and rules:** To factor a cubic polynomial, try to find rational roots using th

1. **State the problem:** We have three different models fitting the decay of a radioactive substance over time $x$ (in days) with amount $y$ (in milligrams). 2. **Identify the mod

1. The problem is to identify the coordinates of point $A$ given as $(-10, 10)$. 2. Coordinates are written as $(x, y)$ where $x$ is the horizontal position and $y$ is the vertical

1. **State the problem:** Solve the inequality $3x - 5 > 1$ for $x$. 2. **Write the inequality:**

1. The problem asks to find the 2nd term in the expansion of $\left(2x^3 - \frac{5}{x^2}\right)^4$ using the binomial theorem. 2. The binomial theorem states that for any integer $

1. **State the problem:** Simplify the expression $$\frac{3}{x-2} - \frac{2}{x-3}$$. 2. **Formula and rules:** To subtract fractions, find a common denominator and combine the nume

1. **State the problem:** Solve for $x$ in the equation $$3^{x+1} = 5^{2-x}$$ and find the value of $x$ step by step. 2. **Recall the formula and rules:** To solve equations with v

1. **State the problem:** Solve for $x$ in the equation $$3^{x+1} = 5^{2-x}$$ and round the answer to the nearest hundredth. 2. **Recall the formula and rules:** To solve equations

1. **State the problem:** We want to find the coefficient of $x^{-5}$ in the expansion of $\left(2x - 3x^{-2}\right)^7$ and determine the value of $k$ corresponding to that term in

1. **State the problem:** We are given the equation $$\frac{-2x - 12}{x (x - 2) (x + 2)} = \frac{A}{x} + \frac{-2}{x - 2} + \frac{-1}{x + 2}$$ and need to find the value of $A$. 2.

1. **State the problem:** Simplify the algebraic expression $$\frac{2}{x-2} + \frac{3}{x^3 - 4x}$$. 2. **Factor the denominator:** Notice that $$x^3 - 4x$$ can be factored by takin

1. **State the problem:** Simplify the expression $$\frac{2}{x^2 - 2x} - \frac{5}{x^2 + x - 6}$$. 2. **Factor the denominators:**

1. **State the problem:** We need to show that there is no constant term (term independent of $x$) in the expansion of $$\left(3x^8 - \frac{3}{x^{15}}\right)^{10}.$$\n\n2. **Recall

1. The problem asks to find the percentage of a journey completed by walking. 2. To find the percentage, use the formula: $$\text{Percentage} = \left(\frac{\text{Distance walked}}{

1. **Problem:** Simplify the algebraic expression $3a(2a - 3b + 4c)$ correctly. 2. **Formula and rules:** Use the distributive property: $a(b + c) = ab + ac$.

1. **State the problem:** Simplify the expression $1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Simplify the expression $$1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7}$$. 2. **Convert mixed numbers to improper fractions:**