🧮 algebra

1. **Problem:** Factor the expression $16n^2 - 9$ completely. 2. **Formula:** Recognize this as a difference of squares: $$a^2 - b^2 = (a + b)(a - b)$$

1. **Problem:** Factor the sum or difference of cubes for the expression $a^3 + 64$. 2. **Formula:** For sum of cubes, use $$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$$

1. **Problem:** Factor the expression $$16n^2 - 9$$ completely. 2. **Formula and rules:** This is a difference of squares, which factors as $$a^2 - b^2 = (a + b)(a - b)$$.

1. **State the problem:** A town has a population of 18000 and grows at 2% every year. We want to find the population after 11 years, rounded to the nearest whole number. 2. **Form

1. **State the problem:** We have a car purchased for 17900 dollars that depreciates at 12.25% per year. We want to find its value after 10 years.

1. **State the problem:** Simplify the expression $$\frac{\frac{3}{2a}}{\frac{4}{3a} - \frac{a}{4}}$$. 2. **Recall the formula:** To divide by a fraction, multiply by its reciproca

1. The problem asks to express the answer as coordinates in terms of $z$. 2. Typically, coordinates in terms of a variable $z$ can be written as $(x, y, z)$ where $x$ and $y$ are e

1. **State the problem:** Solve the system of linear equations for $x$, $y$, and $z$: $$\begin{cases}-3x + 2y - 3z = 4 \\ x + 2y + 3z = 1 \\ 2x + 4y + 6z = 2 \end{cases}$$

1. **State the problem:** Solve the equation $$6(y - 4) = -18$$ for $$y$$. 2. **Use the distributive property:** Multiply 6 by each term inside the parentheses.

1. **State the problem:** Solve the quadratic equation $-x^2 - 6x - 4 = 0$ for $x$. 2. **Rewrite the equation:** Multiply both sides by $-1$ to simplify the leading coefficient.

1. **State the problem:** Solve the equation $4z^2 + 16z = 0$ for $z$. 2. **Formula and rules:** To solve quadratic equations, we can factor the expression and use the zero product

1. **State the problem:** Solve the equation $$12 - 8 = \frac{2}{3}x - 4$$ for $x$. 2. **Simplify the left side:**

1. **State the problem:** Solve the linear equation $$-9 = \frac{2}{7}x + 5$$ for $x$. 2. **Isolate the term with $x$:** Subtract 5 from both sides to get

1. The problem asks to determine the vertex of a parabola given its graph. 2. The vertex of a parabola in the form $y = ax^2 + bx + c$ is given by the formula for the x-coordinate:

1. **State the problem:** A family spends 15 per person for zoo tickets and 5.50 for parking each day. They visit for two days, and the total cost is 191. We need to find the numbe

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 3 to eliminate the d

1. **Problem:** Solve the proportion $$\frac{3}{8} = \frac{15}{x}$$ 2. **Formula:** Cross multiply to solve proportions: $$a/b = c/d \implies ad = bc$$

1. **State the problem:** A town has a population of 7000 and grows at 4% every year. We need to find the population after 13 years, rounded to the nearest whole number. 2. **Formu

1. **State the problem:** Sarah says, "If I subtract 5 from my number, multiply that quantity by 4, and then add 7 to the result, I get 35." We need to write an equation based on t

1. The problem is to simplify the expression where all "x" symbols represent multiplication. 2. Since "x" means multiplication, replace all "x" with the multiplication operator \(\

1. **State the problem:** Simplify the expression using exponent laws. The expression appears to be \(\frac{4a^1 g h x - 3^{2} 2^{2} 2}{6^{9} 2^{h} 2} \times x g h x\). 2. **Rewrit