🧮 algebra

1. **State the problem:** Simplify the expression $x^2 \times x^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, ad

1. The problem involves simplifying algebraic expressions and understanding the floor plan dimensions with tile prices. 2. First, simplify the fraction $$\frac{14x^2 - 63x}{7x}$$.

1. **Stating the problem:** We are given algebraic expressions and a floor plan with dimensions involving $x$. We need to simplify the algebraic fractions and understand the tile d

1. **State the problem:** Expand the expression $ (x+9)(x+8) $. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $$ (a+b)(c+d) = ac + ad + bc + bd $$

1. **State the problem:** Expand the expression $ (x-3)(x+5) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **Problem:** A rectangle has area 6 and perimeter 10. What is the value of its largest side? 2. **Formulas and rules:**

1. **State the problem:** Evaluate the expression $$\sqrt[3]{-8} \times \left(12 - \left(5^2 + \sqrt{9}\right)\right) \div 8$$. 2. **Recall important rules:**

1. The problem asks to factorise the given expressions. 2. Factorisation means expressing an expression as a product of its factors.

1. **State the problem:** Simplify the expression $b \cdot ab^3 \times (-2a^5b)$ where $b = \frac{21m^2n}{7m}$. 2. **Substitute the value of $b$:** Replace $b$ in the expression wi

1. **State the problem:** Calculate the value of $$\sqrt[3]{-8} \times \left(12 - \left(5^2 + \sqrt{9}\right)\right) \div 8$$. 2. **Evaluate the cube root:** $$\sqrt[3]{-8} = -2$$

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