🧮 algebra

1. **Stating the problem:** We need to expand and simplify the following expressions: a) $ (x - y)^2 $

1. **State the problem:** We need to find the value of the expression $6 - 3x$ when $x = -4$. 2. **Write the expression:** The expression is $6 - 3x$.

1. **State the problem:** We need to evaluate the sum $$E \approx t = \sum_{t=5}^{14} \left(50t^{1.6} + 8t\right)$$.

1. **State the problem:** We are given the profit function for a company producing phones: $$P(x) = -1.5x^2 + 10.5x - 4$$

1. **State the problem:** Solve for $x$ in the equation $3(x+9)-(15-x)=8(x+1)$. 2. **Apply the distributive property:**

1. **Problem:** Calculate the products and simplify the radicals as requested. 2. **Step a) Calculate $\sqrt{7} \times \sqrt{8}$:**

1. **State the problem:** We need to complete the description of the piecewise function $f(x)$ based on the graph with three segments:

1. **State the problem:** We need to find the equation of a mystery line given several clues. 2. **Analyze Clue #1:** The mystery line is perpendicular to the line $$y = -\frac{2}{

1. **State the problem:** Solve the equation $$980 = (40) \cdot 8$$. 2. **Understand the equation:** The equation shows a multiplication of 40 and 8 on the right side, which should

1. **State the problem:** We have an arithmetic sequence defined by the rule $x_n = an + b$, where $a$ and $b$ are constants. We need to find $a$ and $b$ given the sequence terms:

1. **State the problem:** Solve the equation $8 \cdot (4 - 40 + 4) = 120$. 2. **Simplify inside the parentheses:** Calculate $4 - 40 + 4$.

1. **State the problem:** Simplify the expression $$\left( \frac{1}{x^2 + xy} + \frac{2}{x - y} - \frac{1}{x^2 - xy} \right) \cdot \frac{x^3 - 2x^2 y + xy^2}{x^2 + xy - y}$$

1. **State the problem:** Find the Least Common Multiple (LCM) of the algebraic expressions $10 + 10x$ and $(2x + 2)(5x - 10)$. 2. **Rewrite expressions to factor form:**

1. **State the problem:** Find the Least Common Multiple (LCM) of the algebraic expressions $(3x + 9)(4x + 4)$ and $7x + 7$. 2. **Rewrite expressions in factored form:**

1. The problem asks to find which equation has a constant of proportionality equal to 4. 2. The constant of proportionality $k$ in an equation of the form $y = kx$ relates $y$ and

1. The problem is to solve any math problem, so let's demonstrate solving a simple algebraic equation: Solve for $x$ in the equation $2x + 3 = 7$. 2. The formula used here is to is

1. The problem is to solve the equation using the Zero-Product Property: $$(x + 7)(4x - 5) = 0$$ 2. The Zero-Product Property states that if the product of two factors is zero, the

1. **State the problem:** Solve the equation $$\frac{3x}{4} - 5 = \frac{x}{2} + 1$$ for $x$. 2. **Write down the equation:** $$\frac{3x}{4} - 5 = \frac{x}{2} + 1$$

1. El problema es resolver una ecuación o expresión matemática paso a paso. 2. Para resolver una ecuación, primero identificamos la ecuación dada (por ejemplo, $ax+b=0$).

1. **State the problem:** Solve the inequality $$4(2x - 3) - 2(5 - 3x) > \frac{x + 4}{2}$$. 2. **Expand and simplify both sides:**

1. **State the problem:** Solve the equation $$\sqrt{x} \times \sqrt{x} \times \sqrt{x} = 6$$. 2. **Rewrite the expression:** Recall that $$\sqrt{x} = x^{\frac{1}{2}}$$. So the lef