🧮 algebra

1. **Stating the problem:** Simplify the expression $Yx + 2y$. 2. **Identify terms:** The expression has two terms: $Yx$ and $2y$.

1. The problem is to simplify the expression $3\sqrt{3} + 6\sqrt{2} - \sqrt{5}$.\n\n2. This expression contains terms with different square roots: $\sqrt{3}$, $\sqrt{2}$, and $\sqr

1. Simplify \( \frac{3x}{6x^2} \). - Factor numerator and denominator: numerator is \(3x\), denominator is \(6x^2 = 6 \cdot x \cdot x\).

1. **State the problem:** Given the formula $a=\frac{4b}{c}$, find the value of $b$ when $a=8$ and $c=5$. 2. **Write down the formula:**

1. **State the problem:** Simplify the expression $$-c^2 + c + c^2 - 4c + 3$$. 2. **Identify like terms:** The terms involving $$c^2$$ are $$-c^2$$ and $$+c^2$$.

1. **State the problem:** Simplify the rational expression $$\frac{4x^2 + 7xy + 3y^2}{16x^2 - 9y^2}$$. 2. **Recall formulas and rules:**

1. **State the problem:** We are given the formula $a=\frac{4b}{c}$ and need to find the value of $b$ when $a=8$ and $c=5$. 2. **Write the formula:**

1. **State the problem:** Simplify the ratio $8:4$. 2. **Formula and rules:** To simplify a ratio, divide both terms by their greatest common divisor (GCD).

1. समस्या को समझें: दो पाइप A और B मिलकर एक टंकी को 36 मिनट में भरते हैं। यदि 30 मिनट बाद पाइप B को बंद कर दिया जाता है, तो टंकी 40 मिनट में भरती है। हमें पाइप B अकेले टंकी को भरने

1. **State the problem:** Simplify and solve the equation $ (7m - 5a) - 4(2n - 3n) = (3n^2 + 2n) $. 2. **Apply the distributive property:**

1. **State the problem:** Solve the linear equation $3x + 9 = 24$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtra

1. Let's start by understanding the problem: we need to find the first few terms of the sequence defined by the formula for the nth term, $u_n = 2n + 1$. 2. The formula $u_n = 2n +

1. **State the problem:** We need to find the first terms of the sequence whose $n^{th}$ term is given by the formula $$u_n = 2n + 1$$. 2. **Formula explanation:** The formula $u_n

1. **State the problem:** Expand and simplify the expression $$(x+5)(x-2)(x+1)$$. 2. **Formula and rules:** To expand a product of polynomials, use the distributive property (also

1. Das Problem: Wir wollen verstehen, wie man mit der Variable $c$ in Gleichungen umgeht und sie Schritt für Schritt löst. 2. Allgemeine Regel: Wenn $c$ in einer Gleichung vorkommt

1. **State the problem:** Solve the linear equation $x - \frac{1}{2} + 3x = 10$ for $x$. 2. **Combine like terms:** The terms with $x$ are $x$ and $3x$. Adding them gives $4x$.

1. **State the problem:** Solve the equation $X - \frac{1}{2} + 3X = 10$ for $X$. 2. **Combine like terms:** The terms with $X$ are $X$ and $3X$, so add them:

1. **State the problem:** Simplify the expression $$(a - 3b) 5a + (2b + 3b + 5b)$$. 2. **Apply distributive property:** Multiply $5a$ by each term inside the first parentheses:

1. **State the problem:** We need to simplify the expression $$\frac{3}{4} + \frac{1}{2} \div 5$$. 2. **Recall the order of operations:** Division and multiplication are performed

1. **State the problem:** Solve the equation $|2x + 3| = 9$. 2. **Recall the definition of absolute value:** For any expression $A$, $|A| = B$ means $A = B$ or $A = -B$ when $B \ge

1. **Problem ①:** Simplify the expression $$-6 - (-3 + 7) + 10$$. 2. **Step 1:** Evaluate inside the parentheses first: $$-3 + 7 = 4$$.