🧮 algebra

1. **Stating the problem:** Simplify the expression $-\left(2\left((1[x-1]1)\right)^2\right) + 5$. 2. **Interpreting the expression:** It seems the expression is $-\left(2(x-1)^2\r

1. **State the problem:** Simplify the expression $$3\left[\left(1[x+4]1\right)^2\right] - 7$$. 2. **Interpret the expression:** The notation is a bit unusual, but it seems to mean

1. **State the problem:** Simplify the expression $$\frac{x^4 - 2x^3 - x + 2}{x - 2}$$ by performing polynomial division. 2. **Recall the formula:** When dividing a polynomial $P(x

1. **State the problem:** Simplify the linear equation $$4a + b + 5 - 2c = 9 - 3c + 3a$$. 2. **Write down the equation:** $$4a + b + 5 - 2c = 9 - 3c + 3a$$.

1. **State the problem:** Simplify the expression $$5x^{-3} y^{2} \cdot (-2x^{-4} y^{-5})$$. 2. **Recall the rules:** When multiplying terms with the same base, add the exponents:

1. **State the problem:** Simplify the linear equation $$-12 - 4c - 16a = -6c - 19a + 2 + 2b$$. 2. **Rewrite the equation:** Move all terms to one side to combine like terms.

1. **Problem statement:** Express the sum or difference of logarithms as a single logarithm. 2. **Formula and rules:**

1. **State the problem:** We need to analyze and understand the function $$f(x) = 5 + \log_2 x$$. 2. **Recall the logarithm properties:** The logarithm $$\log_2 x$$ is defined only

1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n} = 10$$ and solve for $n$. 2. **Write the expression clearly:** The numerator is $n \times n + n = n^2 +

1. **Problem Statement:** We have the quadratic expression $4x^2 + bx - 45$, where $b$ is a constant. It can be factored as $(hx + k)(x + j)$, where $h$, $k$, and $j$ are integers.

1. **Stating the problem:** Factor the polynomial $$a^2 + 3b^2 + 4ab + 2ac + 6bc - 4b + 4c - 4$$ using $a$, $b$, or $c$ as the variable. 2. **Choosing variable $a$ to factor:** Gro

1. **Problem statement:** Factor the expression $$ab + 2ac + 3b^2 + 6bc - 5a - 13b + 4c - 10$$ 2. **Exercise (1) with variable $a$:**

1. **State the problem:** We are given the quadratic equation $$x^2 - 2x - 9 = 0$$ and told one solution can be written as $$1 + \sqrt{k}$$. We need to find the value of $$k$$. 2.

1. The problem asks to solve number 2, but no specific problem statement was provided. 2. Please provide the exact problem or equation for number 2 so I can solve it accurately.

1. **Stating the problem:** We are given two linear equations:

1. **Problem statement:** Factor the expression $$ab + 2ac + 3b^2 + 6bc - 5a - 13b + 4c - 10$$ We will arrange and factor it first with respect to variable $a$, then with respect t

1. **State the problem:** Solve the equation $x(x + 1) - 56 = 4x(x - 7)$ and find the sum of its solutions. 2. **Write the equation:**

1. **Problem (a):** A businessman sold a refrigerator for 2745 making a profit of 15% on the cost price. Find the cost price. 2. **Formula:** Profit% = \frac{Selling Price - Cost P

1. **Stating the problem:** Simplify the expression $$4 - 8 \div \frac{2}{3}$$ and evaluate the division $$\frac{1}{2} \div \frac{1}{2}$$. Also, interpret the handwritten note $$6

1. **State the problem:** We are given the cost function $NC = 3.02(x^2 + 200)^{0.02}$ and the revenue function $NR = (2\sqrt{x} + 1) + 1.75$. We want to find the profit function $

1. **State the problem:** Solve each system of equations using substitution. Identify which three systems have the solution $(4,16)$ and unscramble their letters to find a secret c