🧮 algebra

1. The problem states the identity $a^2 - b^2 = (a - b)(a + b)$. 2. This is a difference of squares formula, which says that the difference between two squares can be factored into

1. The problem asks for the end behavior of the polynomial function $$p(x) = 4x^8 - 6x^7 + 3x^3 - 10.$$\n\n2. To determine end behavior, focus on the leading term of the polynomial

1. **State the problem:** Solve the quadratic equation $$-6x^{2} + 17x - 5 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^{2} + bx + c = 0$$ is

1. **Problem Statement:** Simplify the expression $9x^5 y^2 x - 2x^{-2} y^{-2}$. 2. **Recall the laws of exponents:**

1. **State the problem:** Simplify the expression $9x^5 y^2 \times (-2x)^{-2} y^{-2}$. 2. **Recall the rules:**

1. **State the problem:** We are given the simultaneous equations:

1. **State the problem:** Simplify the expression $9 x^{5} y^{2} x - 2 x^{-2} y^{-2}$. 2. **Rewrite the expression:** Combine like bases with exponents where possible.

1. The problem is to find the equation of a line with a given gradient (slope) of $-2$. 2. The general formula for the equation of a line in slope-intercept form is:

1. **State the problem:** Calculate $$\frac{3^2 \times 3}{3^4 + 3 \times 27}$$. 2. **Recall the rules:**

1. Masalah: Tentukan persamaan garis yang melalui titik $A(3,-4)$ dengan gradien $2$. 2. Rumus yang digunakan: Persamaan garis dengan gradien $m$ yang melalui titik $(x_1,y_1)$ ada

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y = 6 \\ x - y = 2 \end{cases}$$

1. Masalah: Tentukan persamaan garis yang melalui titik A (0,4) dengan gradien 2. 2. Rumus yang digunakan adalah rumus persamaan garis dengan gradien (m) dan titik (x_1,y_1):

1. **State the problem:** Simplify the radical expression $\sqrt{75}$.\n\n2. **Recall the formula and rules:** To simplify a square root, find the prime factorization of the number

1. **State the problem:** Solve the inequality $$\sqrt{2x - 4} + \sqrt{x + 4} \geq \sqrt{2x}$$. 2. **Identify domain restrictions:**

1. **State the problem:** Solve the inequality $$\sqrt{2x - 3} + \sqrt{4x - 2} \leq \sqrt{6x - 5}$$. 2. **Identify domain restrictions:**

1. **Stating the problem:** Simplify and analyze the function $$y = \tan^8 x - 4x^2 \sec x - x^{\cos x}$$. 2. **Recall the definitions and properties:**

1. **Stating the problem:** Solve the equation or task given (since the user only said "solve 1 task" without specifying, we assume a generic example: solve $x^2 - 4 = 0$. 2. **For

1. The problem is to solve the equation $1 = 1$. 2. This equation states that the number 1 is equal to the number 1.

1. **State the problem:** Simplify or analyze the expression $$(n - 1)(x + 2) \sqrt{x^4 + 3x^3 - x^2 + x + 2}.$$\n\n2. **Understand the components:** The expression is a product of

1. The problem is to divide two numbers or expressions, but the exact division is not specified. 2. Division in algebra is performed by writing one expression over another as a fra

1. **State the problem:** Simplify the expression $$(x - 1)(x + 2) \sqrt{x^4 + 3x^3 - x^2 + x + 2}$$ 2. **Recall the formula and rules:**