🧮 algebra

1. The problem asks to factorize the expression $-2a^2$. 2. Factorization means expressing the expression as a product of its factors.

1. **State the problem:** Factor the polynomial $x^3 - 216$. 2. **Recognize the form:** This is a difference of cubes since $216 = 6^3$.

1. **Stating the problem:** Simplify the algebraic expressions and solve the given rational expressions involving $x$. 2. **Expression 1:** Simplify $\frac{14x^2 - 63x}{7x}$.

1. **State the problem:** Factor the perfect square trinomial $$289x^2 + 34x + 1$$. 2. **Recall the formula for a perfect square trinomial:**

1. **Problem statement:** We are given points $C(3, -6)$ and $D(-2, 4)$.

1. **State the problem:** We need to solve the equation $$68 = x$$ for the variable $x$. 2. **Understand the equation:** The equation is already in the form where $68$ equals $x$.

1. **State the problem:** Determine the slope of line CD given points C(3, -6) and D(-2, 4). 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}-8x + 2y = 14 \\ y + 2x = -5 \end{cases}$$

1. **State the problem:** We need to find the value of $x$ given the equation $x = 68x$. 2. **Write down the equation:**

1. **State the problem:** We need to find the constant of proportionality $k$ in the proportional relationship between the number of chocolates Miranda buys, $x$, and the number of

1. **Stating the problem:** Stéphanie wants to renovate her kitchen floor with ceramic tiles around a square island. We need to find a tile size that fits her budget of 1000 and me

1. **State the problem:** Approximate the square roots of given numbers using nearby perfect squares and interpolation. 2. **Recall the perfect squares:**

1. **Stating the problem:** Simplify the expression $$\frac{-10x^2 - 40x^2}{2x^2 - 8x}$$. 2. **Combine like terms in the numerator:**

1. **Stating the problem:** We have five pentagons, each with 5 numbers at vertices. Inside each pentagon is a number that is the sum of two other numbers from that pentagon. We ne

1. **Problem:** Identify the correct values of labeled points P, Q, R, and S on the number line given their square roots. 2. **Step:** Calculate approximate values of each square r

1. **State the problem:** Expand the expression $6e + 15$. 2. **Understand the expression:** The expression consists of two terms: $6e$ and $15$. Here, $e$ is the mathematical cons

1. **State the problem:** Solve the equation $4x = 20$ using a bar model. 2. **Understand the equation:** The equation $4x = 20$ means four equal parts (each of size $x$) add up to

1. The problem is to evaluate the expression $6e + 15$ where $e$ is the mathematical constant approximately equal to 2.71828. 2. Recall that $e$ is the base of the natural logarith

1. The problem is to graph the inequality $y < -\frac{1}{5}x - 1$. 2. This inequality represents all points below the line $y = -\frac{1}{5}x - 1$.

1. **State the problem:** We need to complete the table showing the pieces of bamboo Ling Ling eats over time, where the pieces eaten each minute are represented as a multiplicatio

1. **State the problem:** We have two taxi services with different pricing schemes: