🧮 algebra

1. **Stating the problem:** Simplify the expression $$(7b^5 - 4b)(7b^5 + 4b)$$. 2. **Recognize the pattern:** This is in the form of $$(x - y)(x + y) = x^2 - y^2$$ where $$x = 7b^5

1. We are asked to add the fractions $\frac{3}{2}$ and $\frac{25}{16}$. 2. To add fractions, they must have a common denominator. The denominators here are 2 and 16.

1. **State the problem:** Given the expansion of $$(ax - 2)^4 \left(1 + \frac{b}{x}\right)^3$$ written in descending powers of $x$, the first three terms are $$81x^4 + 999x^3 + cx^

1. Stating the problem: We need to find a solution to the user's math question. However, no explicit problem statement was provided. 2. Since the user only asked for a "correct sol

1. Stating the problem: We need to simplify each expression under the square root, breaking it down into factors with perfect squares and variables with even powers so we can simpl

1. The problem is to simplify the expression $\frac{-5}{2} \times \frac{1}{2}$.\n\n2. Multiply the numerators together: $-5 \times 1 = -5$.\n\n3. Multiply the denominators together

1. We are given the system of equations: $$\begin{cases} x + 2y + z = 7 \\ x + \alpha z = 11 \\ 2x - 3y + \beta z = \gamma \end{cases}$$

1. The problem is to factor the quadratic expression $9x^2 + 5x - 80$. 2. We look for two numbers that multiply to $9 \times (-80) = -720$ and add to $5$.

1. The problem states: Find the range of the relation $R_2 = \{(1,0),(2,2),(3,2),(4,2)\}$.\n\n2. The range of a relation is the set of all possible output values (second elements)

1. نبدأ بكتابة الدالة المعطاة: $$k(x) = 8 - 3\sqrt{x} + 2$$

1. Let's start by understanding what domain and range mean. The domain of a relation is the set of all possible input values (x-values), and the range is the set of all possible ou

1. **Problem:** Sheila has 25000 to invest and wants to earn 12000 interest at 5.8% per year. Find the time (years). 2. **Formula for simple interest:** $$I = P \times r \times t$$

1. **State the problem:** We are given a straight line when plotting $e^y$ against $x^2$, with gradient $-3$ passing through $(4.30,5.85)$. We need to: (a) Find $y$ in terms of $x$

1. **State the problem:** We have a plot of $e^y$ versus $x^2$ that forms a straight line with gradient $-3$. The line passes through the point $(4.30, 5.85)$. We need to find (a)

1. **Problem:** Aiko earns ₱15 500 monthly plus 8% commission on all her sales. She sold a car worth ₱1 550 000 last month. Find her total earnings last month. Step 1: Calculate th

1) **Problem:** Calculate the interest earned on a savings deposit of 17800 at an annual interest rate of 5.5% after 3 years. **Given:**

1. Problem 1: Loremea received a 5% discount which saved her ₱634.50. We need to find the original price (let's call it $P$). Discount = 5% of original price = $0.05P$

1. Problema: Sergio tiene 7 años y su papá 32 años. ¿Dentro de cuántos años la edad del padre será el doble de la de su hijo? 2. Sea $x$ los años que pasarán para que la edad del p

1. The problem is to find the square root of 43.09. 2. Recall that the square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. We are asked to find the square root of 474. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Simplify the expression $$\frac{5}{y} - \frac{1}{4} + \frac{3y}{4} + \frac{1}{2}$$. 2. **Group like terms:** The expression has terms with $y$ in the deno