🧮 algebra

1. **Factorise** $2c^2 - 8cm - 3cm + 12m^2$. 2. **Find the coefficient of** $n$ in $(4n + 3)(n - 5) - (2n - 3)^2$.

1. **Stating the problem:** Calculate 7% of 25. 2. **Formula used:** To find a percentage of a number, use the formula:

1. The problem asks to solve example number 2, but since no specific problem statement was provided, I will assume you want a general approach to solving algebraic equations. 2. Ty

1. **State the problem:** Simplify the expression $$\frac{\left(x^{-\frac{1}{3}} \cdot \sqrt[3]{x^2}\right)^3}{x^{-2}}$$. 2. **Recall the rules:**

1. **State the problem:** Donneth wants to invest a total of 100000 in life insurance and a bank account. 2. **Define variables:** Let $x$ be the amount invested in life insurance

1. **State the problem:** We want to prove the upper bound of the function $$f(x) = \frac{x}{x^2 - x}$$ for $$x \in (2, \infty)$$. 2. **Rewrite the function:** Simplify the denomin

1. **State the problem:** Simplify the expression $$(4\sqrt{5})^2 + 2^{-3} - 67^0 - \sqrt[3]{\frac{27}{8}}$$. 2. **Recall important rules:**

1. **State the problem:** Solve the equation $2x - 5 = 3x + 7$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the inequality $x^2 - 14x > 0$. 2. **Rewrite the inequality:** Factor the left side:

1. **Problem 7:** Simplify the expression $ (5 - 2x^3 - 6x) - (2x^4 - 2x^2 + 5x^3 - 5) - (6x^3 + x^2 + 1 + 4x) $. 2. Write the expression without parentheses, changing signs for th

1. **State the problem:** We need to find the missing fraction $x$ in the equation $$1 - x = \frac{1}{3} + \frac{3}{12}.$$\n\n2. **Combine the fractions on the right side:** First,

1. **Problem Statement:** Match the descriptions of the parabolas to their graphs and estimate the roots from the graphs.

1. **Stating the problem:** We need to find the amount of sugar mixture used in the cake after setting aside 1/4 cup for the crumb topping. 2. **Given quantities:**

1. The problem asks to find which expressions have a sum or difference equal to $\frac{3}{4}$.\n\n2. We will evaluate each expression by finding a common denominator and simplifyin

1. The problem is to find the difference between the fractions $\frac{7}{8}$ and $\frac{1}{3}$.\n\n2. To subtract fractions, we need a common denominator. The denominators are 8 an

1. Let's start by stating the problem: You want to understand what a quadratic equation is and how to solve it. 2. A quadratic equation is any equation that can be written in the f

1. **State the problem:** We have the function $$g(x) = 7 + \frac{6}{5}x - 1$$ with domain restriction $$x \neq 1$$. We need to find:

1. Stating the problem: Simplify the expression $ (3)(4) + \left((4)(5) - (1)(2)\right) \frac{3}{8} $. 2. Calculate the products inside the parentheses:

1. **Stating the problem:** We have a piecewise function defined as: $$g(x) = \begin{cases} 3^x - \sqrt{x} & \text{for } x \in (0,1) \\ x - 5 + \log_2(x-1) & \text{for } x \in (1,3

1. The problem asks to find the sum of the word "answer" plus a number. 2. Since "answer" is a word and cannot be added to a number mathematically, we interpret the question as con

1. The problem is to explain how the sum \(\sum_{t=1}^4 (1+0.06)^t \times 500\) is simplified to \(500 \times \left( \frac{0.06}{1 - (1.06)^{-4}} \right)\). 2. This sum is a geomet