🧮 algebra

1. The problem is to simplify the expression $b^2$. 2. This expression represents the square of the variable $b$, which means $b$ multiplied by itself.

1. **State the problem:** We are given variables $a=3$, $b=4$, $c=\frac{1}{2}$, and $d=100$. We need to solve the following expressions:

1. **Stating the problem:** Simplify the expression $$\frac{a-4}{4a^2-16} + \frac{968+2a^2+a}{a^4-16} \cdot \frac{a-2}{a^2+a} - \frac{4-6a}{a^4+2a^3+a^2}.$$ 2. **Factor all denomin

1. **State the problem:** We are asked to fill in blanks and evaluate expressions involving directed numbers (positive and negative integers), absolute values, and inequalities. 2.

1. **State the problem:** Evaluate the expression $12 + (-2)(-3)(42)$. 2. **Recall the rules:** Multiplication of two negative numbers results in a positive number.

1. **State the problem:** Write an equation in point-slope form for a line with slope $\frac{3}{5}$ passing through the point $(-2, 6)$. 2. **Recall the point-slope form formula:**

1. The problem asks us to write the equation of a line in slope-intercept form given the slope and y-intercept. 2. The slope-intercept form of a line is given by the formula:

1. The problem asks to simplify the expression $$\frac{32^3}{32^8}$$ and compare it to the options given. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^

1. The problem asks to simplify the expression $5^4 \cdot 5^7$ in exponential form. 2. Recall the rule for multiplying powers with the same base: $$a^m \cdot a^n = a^{m+n}$$ where

1. **State the problem:** Solve the quadratic equation $4x^2 - 1 = 0$ for $x$. 2. **Formula and rules:** This is a quadratic equation in the form $ax^2 + bx + c = 0$. Here, $a=4$,

1. Stated problem: Simplify and evaluate the expression $ (a - 1)^2 - (a + 1)(a - 1) $. 2. Use the formulas:

1. **State the problem:** Two classes, Class A and Class B, sell tickets for a movie night. Each ticket costs 5, and each class pays a 20 fee. Class B sells three times as many tic

1. **State the problem:** We need to divide the polynomial $x^3 - 2x^2 + 1$ by the binomial $x - 1$. 2. **Recall the formula:** Polynomial division can be done using long division

1. **Stating the problem:** Izračunajmo izraz $\left(\frac{1}{2} + a\right)^2$.

1. **Planteamiento del problema:** Se nos piden realizar operaciones de suma y resta entre matrices dadas. 2. **Reglas importantes:** Para sumar o restar matrices, deben tener las

1. **State the problem:** A store pays 18 for a teapot and marks up the price by 40%. We need to find the amount of the mark-up. 2. **Formula:** The mark-up amount is calculated by

1. **State the problem:** Juan's bill was 27 and he left a 20% tip. We need to find the amount of the tip. 2. **Formula:** Tip amount = (Percentage tip) \times (Bill amount)

1. **Problem:** Solve the equation $5 \cdot (x + 1) = 10 - 3 \cdot x$ for $x$. 2. **Formula and rules:** Use the distributive property $a(b+c) = ab + ac$ to expand expressions.

1. The problem asks if the ratios $\frac{11}{14}$ and $\frac{6}{7}$ form a proportion. 2. Two ratios form a proportion if they are equal, i.e., if

1. **State the problem:** Solve the equation $8 \div 2(4 - x) = 1$ for $x$. 2. **Recall the order of operations:** Division and multiplication have the same precedence and are eval

1. **State the problem:** Calculate the expression while keeping fractions in their fractional form. 2. **Formula and rules:** When performing arithmetic with fractions, use the fo