🧮 algebra

1. **State the problem:** Simplify the expression $5(x+y)-2(x-y)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Valeria spent a total of 21 on 8 games and rides. Each game costs 1.50 and each ride costs 3. We want to find the number of games $x$ and rides $y$. 2. **

1. **State the problem:** A jeweler has a fixed amount of gold and makes bracelets and necklaces. Each bracelet uses 7 grams of gold, each necklace uses 18 grams, and the total gol

1. **State the problem:** Solve the inequality $$5h + 5(9h + 1) \leq 5h + 1 - 2$$ for $h$. 2. **Apply the distributive property:** Multiply $5$ by each term inside the parentheses:

1. **Problem:** Find the first 4 terms in the power series expansion of $$f(x) = \frac{(1+2x)^2}{(1-x)^2}$$ and state when the expansion is valid. 2. **Formula and rules:**

1. The problem is to find the square root of 81. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to simplify the expression $$\frac{n \times n + n}{n}$$ and find its value when $n=10$. 2. The formula involves algebraic simplification of fractions. Important r

1. **State the problem:** Solve the equation $x^2 = 16$ for $x$. 2. **Formula and rules:** To solve equations of the form $x^2 = a$, where $a$ is a positive number, we use the squa

1. **State the problem:** Solve the equation $x^2 + 27 = -12x$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the quadratic equation $x^2 + 4x = 5$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. Muammo: $y = \sqrt{|x|} - 3 + \frac{1}{\sqrt{10 - x}}$ funksiyasining aniqlanish sohasini topish. 2. Aniqlanish sohasini topish uchun har bir ifodaning aniqlanish shartlarini ko

1. The problem is to understand why the solutions to $x^2 = 81$ are both positive and negative 9. 2. The key formula is that if $x^2 = a$, then $x = \pm \sqrt{a}$, meaning both pos

1. The problem is to solve the equation $x^2 = 81$. 2. The formula used here is to take the square root of both sides to solve for $x$. Remember, when you take the square root of b

1. Muammo: $y=\sqrt{\frac{x^2}{|x|-3}}$ funksiyaning aniqlanish sohasini topish. 2. Aniqlanish sohasini topish uchun, ildiz ostidagi ifoda manfiy bo'lmasligi kerak va maxraj nolga

1. Problem: Solve the inequalities given. 2. Formula and rules: For quadratic inequalities of the form $ax^2 + bx + c > 0$, $\geq 0$, $< 0$, or $\leq 0$, first find the roots by so

1. **State the problem:** Solve the equation $x^3 = 8$ for $x$. 2. **Formula and rules:** To solve for $x$ when given $x^3 = a$, use the cube root: $x = \sqrt[3]{a}$.

1. **Problem statement:** Consider the function $f(x) = 2x^2 - 3x + 1$. We need to find: 1) The domain of definition of $f(x)$.

1. The problem is to simplify the expression $$\frac{81}{9^{2 - 3x}}$$ given that $$y = 3^x$$. 2. First, express 81 and 9 in terms of base 3 because 81 and 9 are powers of 3:

1. **State the problem:** Simplify the expression $$\sqrt{32x^4} \cdot \sqrt{50x^2} \cdot \sqrt{2x^3}$$ so that the radicand has no perfect squares except for 1. 2. **Recall the pr

1. Let's start by understanding the problem: FPM usually stands for 'Fraction, Percentage, and Multiplication' or could relate to 'Forming and Solving Equations' in Edexcel IGCSE m

1. Problem: Simplify the rational expression $\frac{6x^2 y^2}{8xy^5}$. 2. Formula and rules: To simplify a fraction, divide numerator and denominator by their greatest common facto