🧮 algebra

1. The problem is to multiply $2x$ by $x$. 2. Recall that when multiplying terms with the same base, you add the exponents: $x^1 \times x^1 = x^{1+1} = x^2$.

1. **State the problem:** We are given the equation $$x^2 \sqrt{x^2 - c^2} = c^2 \sqrt{x^2 - c^2} + 39$$ where $c$ is a positive constant. We need to find one of the solutions for

1. **State the problem:** Factorize fully the expression $$15y^4 + 20xy^3$$. 2. **Identify the greatest common factor (GCF):**

1. **State the problem:** Factorize the expression $4c - 14$. 2. **Identify the common factor:** Both terms $4c$ and $14$ have a common factor of $2$.

1. The problem is to multiply $3x^2$ by $2x^2$. 2. Multiply the coefficients: $3 \times 2 = 6$.

1. The problem is to understand the number 0.14 and its properties. 2. 0.14 is a decimal number representing fourteen hundredths.

1. The problem is to round the number 0.009876 to 3 decimal places. 2. Identify the digit at the third decimal place: 0.009876 has digits 0 (1st decimal), 0 (2nd decimal), and 9 (3

1. **State the problem:** We are given the function $$F(x) = x^{\frac{4}{5}} (x - 4)^2$$ and want to understand its behavior. 2. **Rewrite the function:** The function is a product

1. The problem is to simplify or factor the expression $9t^2 - u^2$. 2. Recognize that this is a difference of squares, which follows the formula $a^2 - b^2 = (a - b)(a + b)$.

1. Let's first understand what a binary operation is. A binary operation on a set is a rule for combining any two elements of the set to form another element of the same set. 2. Fo

1. Let's start by defining what a binary operation is. 2. A binary operation on a set $S$ is a rule that combines any two elements $a$ and $b$ from $S$ to produce another element i

1. The problem is to simplify or factor the expression $12n^2 - 4mn$. 2. First, identify the greatest common factor (GCF) of the terms $12n^2$ and $4mn$.

1. **State the problem:** Simplify the expression \n\n$$\frac{5x^2 + 6x - 8}{x^2 + 9x + 14} \div (x^2 - 4)$$\n\n2. **Rewrite the division as multiplication by the reciprocal:**\n\n

1. **State the problem:** Convert the recurring decimal $1.237$ (where $7$ is recurring) into a fraction. 2. **Define the decimal:** Let $x = 1.237777\ldots$ where the digit $7$ re

1. The problem is to convert the recurring decimal $0.237237\ldots$ into a fraction. 2. Let $x = 0.237237237\ldots$ where the block "237" repeats indefinitely.

1. **State the problem:** We are given the function $$f(x) = \sqrt{\frac{x+2}{x-2}}$$ and need to find the value(s) of $$x$$ such that $$f(x) = 3$$. 2. **Set up the equation:** Sub

1. The problem states that the average number of magazines sold per day in a week is 4. 2. There are 7 days in a week, so the total number of magazines sold in a week is $7 \times

1. The problem gives the equation $$4a - 2b = 10$$ and asks for the value of expressions involving $a$, $b$, and $c$. 2. (a) Find the value of $$2a - b$$.

1. **State the problem:** Solve the equation $$\frac{3x}{5} = \frac{2x - 9}{5}$$ for $x$. 2. **Observe the denominators:** Both sides have the same denominator 5, so we can multipl

1. State the problem: Solve for $x$ in the equation $$\frac{3x}{5} = 2x - \frac{9}{5}.$$\n\n2. Eliminate the fractions by multiplying every term by 5 to clear the denominators:\n$$

1. **State the problem:** Given the equations $ab + ac + bc = 8$ and $abc = 4$, find the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$. 2. **Recall the expression for the sum