🧮 algebra

1. The problem is to simplify the expression \( x^2 - 8xy \). 2. This expression consists of two terms: \( x^2 \) and \( -8xy \).

1. State the problem: Simplify the expression $\frac{6x - 4}{2} + \frac{20x + 25}{5}$.\n\n2. Simplify each term separately:\n- Divide $6x - 4$ by 2: $$\frac{6x - 4}{2} = \frac{6x}{

1. **State the problem:** Simplify the expression $$\frac{6x - 4}{2} + \frac{20x + 25}{5}$$

1. State the problem: We want to solve the equation $y = y^2$ for $y$. 2. Rearrange the equation to bring all terms to one side:

1. **Problem statement:** Solve the quadratic equation $x^2 + 6x + 5 = 0$ by completing the square. 2. **Step 1: Move constant to the other side.**

1. We are given the equation $\frac{3}{x+2} - \frac{1}{x} = \frac{1}{5x}$.\n2. To solve this equation, first find a common denominator for the terms on the left. The denominators a

1. Let's start by stating the problem: solve the quadratic equation by completing the square. 2. Consider a quadratic equation in the form $$ax^2 + bx + c = 0$$ where $$a \neq 0$$.

1. **State the problem:** We need to evaluate the expression $$4(x^2 - 1) + \frac{x^3}{4} + 12$$ when $$x = -2$$.

1. We are asked to solve the quadratic equation $4x^2 + ? = 0$ (assuming the general form $ax^2 + bx + c = 0$). 2. To proceed, I'll demonstrate solving a quadratic equation by two

1. Given the equation $a - \frac{1}{a} = 3$, find the value of $\frac{5a}{a^{2} + 2a - 1}$. Step 1: Multiply both sides of the equation by $a$ to clear the fraction:

1. Stating the problem: Siew Ling gave 40% of her salary to her father. He spent 75% of that amount on food and had 180 left. We need to find Siew Ling's total salary. 2. Let S be

1. **State the problem:** Simplify the expression $$\frac{\left(\sqrt{125a^5}b^{-3}\right)^{-3}}{5ab^{-1}}$$. 2. **Simplify inside the numerator:**

1. Stating the problem: Simplify the expression $$\sqrt{125a^2b^{-3}} \div 5ab^{-1}$$. 2. Simplify the square root: $$\sqrt{125a^2b^{-3}} = \sqrt{125} \cdot \sqrt{a^2} \cdot \sqrt{

1. Stating the problem: Simplify the expression $$\frac{\sqrt{125a}^5 b^{-3}}{5ab^{-1}}$$. 2. Rewrite the square root as an exponent: $$\sqrt{125a} = (125a)^{\frac{1}{2}}$$.

1. **State the problem**: Simplify the expression $$\frac{\sqrt{125a^2b}^{-3}}{5ab^{-1}}.$$\n\n2. **Rewrite the expression**: The numerator is $\left(\sqrt{125a^2b}\right)^{-3}$ an

1. The problem is to explain what a linear equation is. 2. A linear equation is an algebraic equation of the form $ax + b = 0$, where $a$ and $b$ are constants and $x$ is the varia

1. The user request is unclear and does not present a specific algebra problem to solve. 2. Without a concrete algebraic expression or question, we cannot perform algebraic manipul

1. The problem is to find the value of $16^{0.25}$. 2. Recall that raising a number to the power 0.25 is the same as taking the fourth root of that number because $0.25 = \frac{1}{

1. The given expression is a fraction: $\frac{-16}{24}$. 2. To simplify this fraction, find the greatest common divisor (GCD) of 16 and 24.

1. State the problem: Find the smallest prime number $x$ such that $3 - 4x < -41$. 2. Solve the inequality:

1. Muammoni bayon qilamiz: $$\sqrt{2} - 2 - \sqrt{1} - 4\sqrt{9} - \sqrt{80}$$ ifodasining qiymatini topish. 2. Har bir ildiz ifodalarini hisoblaymiz: