🧮 algebra

1. **State the problem:** Expand the expression $ (2x-1)(x-6) $. 2. **Recall the distributive property (FOIL method):**

1. **State the problem:** Simplify the expression $6(x-2)-4(x-8)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Simplify the expression $y - 4m - 3y - 5m$. 2. **Group like terms:** Combine the terms with $y$ and the terms with $m$ separately.

1. **State the problem:** Simplify the expression $Y - 4m - 3y - 5m$. 2. **Identify like terms:** The terms involving $m$ are $-4m$ and $-5m$.

1. **Problem statement:** Simplify the algebraic expression $2x - 2y - 6x + 5y$. 2. **Formula and rules:** Combine like terms by adding or subtracting coefficients of the same vari

1. **Problem 3: Factor using the difference of squares** The difference of squares formula is:

1. **Enunciato del problema:** Dato il fascio di rette definito dall'equazione $$(2K+1)X + 3KY + 1 + K = 0,$$ dobbiamo:

1. **Problem statement:** Given the quadratic equation $x^2 - px + q = 0$ with roots $\alpha$ and $\beta$, find the quadratic equation whose roots are $\alpha^2 + \frac{1}{\beta^2}

1. Let's clarify the problem: You want to understand why the minimum value of a function is not less than -2. 2. Typically, to find the minimum value of a function, we analyze its

1. The problem asks to convert 12°F to Celsius using the formula $$C = \frac{5}{9}(F - 32)$$ and round to the nearest tenth. 2. Substitute $F = 12$ into the formula:

1. **Problem Statement:** Find the angle between the two lines given by the equations: $$x + 7y - 3 = 0$$

1. **Problem statement:** Find the values of $a$ and $b$ for the cubic curve $$y = x^3 + ax^2 + bx + 3$$ given that it passes through the point $(1,8)$ and the tangent line at that

1. The problem is to find the domain of the function $f(x) = x^2 + 5x + 6$. 2. The domain of a function is the set of all possible input values ($x$) for which the function is defi

1. **State the problem:** We need to find the value of $b$. 2. **Identify given information:** Since the problem only states "find b" without additional context, we assume there is

1. **State the problem:** Simplify the expression $20\sqrt{20} \div 4\sqrt{4}$. 2. **Recall the properties:** The square root of a product can be separated as $\sqrt{a} \times \sqr

1. Stating the problem: Simplify the expression $\sqrt{5} \times \sqrt{11}$. 2. Formula used: The product of square roots rule states that $\sqrt{a} \times \sqrt{b} = \sqrt{a \time

1. The problem asks to convert 12°F to Celsius using the formula: $$C = \frac{5}{9} (F - 32)$$

1. The problem is to evaluate the expression $7x + 2y + \frac{x}{2}$ when $x=2$ and $y=4$. 2. The expression is a linear combination of $x$ and $y$ with an additional fractional te

1. **State the problem:** We need to find the distance between a bird flying 3500 m above sea level and a diver 40 m below sea level. 2. **Understand the positions:** The bird is a

1. **State the problem:** Evaluate the expression $3 \times (-3)^2 \times 10^0$. 2. **Recall the rules:**

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{-6} = 6.$$\n\n2. **Formula and rule:** To isolate $x$, multiply both sides of the equation by $-6$ (the denominat