🧮 algebra

1. **State the problem:** We need to find the product of the two polynomials $2x^4 + 3x^2$ and $x^4 - x^2$. 2. **Formula used:** To multiply two binomials, use the distributive pro

1. **Problem:** Calculate $0.8 - 0.206$. **Step 1:** Write the subtraction.

1. The problem is to understand the expression $f(6*7x)$ and simplify it if possible. 2. The expression inside the function is $6*7x$. According to the order of operations, multipl

1. **State the problem:** Simplify the expression $$\frac{\frac{6}{u+1} + \frac{3}{u-5}}{\frac{5}{u+1}}$$. 2. **Rewrite the complex fraction:** The expression is a fraction divided

1. **State the problem:** Simplify the expression $$27x - 62 - 12c + 27 + (-28)c - 11x + 26x - 27$$. 2. **Group like terms:** Group the terms with $x$, $c$, and constants separatel

1. **State the problem:** We want to learn how to simplify equations. 2. **Formula and rules:** Simplifying equations involves combining like terms, using distributive property, an

1. **State the problem:** Solve the equation $$5x + 81 = x - 344$$ for $$x$$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one sid

1. ปัญหาคือหาค่าของ $S/22560 - 90$ โดยที่ $S$ ไม่ได้กำหนดไว้ในโจทย์นี้ จึงต้องสมมติหรือหาค่าของ $S$ ก่อน 2. เนื่องจากไม่มีข้อมูลเพิ่มเติมเกี่ยวกับ $S$ ในข้อความที่ให้มา จึงไม่สามาร

1. **State the problem:** Solve the equation $$A = 4x^2 + 8xh$$ for the variable $$x$$. 2. **Write the equation:** $$A = 4x^2 + 8xh$$.

1. **State the problem:** We are given the formula for the area of a triangle as $$A = \frac{1}{2} bh$$ and need to find the correct formula for the height $h$ in terms of $A$ and

1. **State the problem:** Evaluate the expression $$\dfrac{17}{6^2} - \dfrac{5}{9 \cdot 4}$$ without rounding the answer. 2. **Recall the formula and rules:** We need to simplify e

1. **State the problem:** Evaluate the expression $$\dfrac{-12}{-4 - 8}$$. 2. **Simplify the denominator:** Calculate $$-4 - 8$$.

1. **State the problem:** We are given a point $(1,k)$ that lies on the curve $c$. We need to find two possible values of $k$. 2. **Identify the curve $c$:** Since the curve $c$ is

1. The problem is to find the formula for the difference of squares. 2. The difference of squares formula states that for any two variables or numbers $a$ and $b$, the expression $

1. **State the problem:** Find two numbers whose sum is $\frac{1}{4}$ and whose product is $-\frac{1}{8}$. 2. **Use the quadratic equation approach:** Let the two numbers be $x$ an

1. The problem is to understand the value and meaning of the fraction $-\frac{1}{8}$. 2. A fraction $\frac{a}{b}$ represents division of $a$ by $b$, where $a$ is the numerator and

1. **State the problem:** Find two numbers whose sum is $\frac{1}{4}$ and whose product is $-1.8$. 2. **Use the formulas:** Let the two numbers be $x$ and $y$. Then:

1. **State the problem:** We need to add $\frac{1}{4}$ and multiply by $\frac{1}{8}$. The problem can be interpreted as either $(\frac{1}{4} + x) \times \frac{1}{8}$ or simply addi

1. **State the problem:** Solve for $x$ in the equation $$\frac{3x}{4} + 2 = 4x - 1$$. 2. **Write down the equation:** $$\frac{3x}{4} + 2 = 4x - 1$$.

1. **State the problem:** Solve the equation $$\frac{5}{6} q - \frac{1}{2} = \frac{3}{8}$$ for $q$. 2. **Add $\frac{1}{2}$ to both sides** to isolate the term with $q$:

1. **State the problem:** We want to factor the quadratic expression $$x^2 - x + \frac{2}{9}$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for