🧮 algebra

1. **State the problem:** Factor the expression $x^2 - 16$. 2. **Recall the formula:** This is a difference of squares, which follows the rule:

1. **State the problem:** Given the parabola equation $$(x + 2)^2 = -12(y - 5),$$ find the vertex, focus, endpoints of the latus rectum, and the equation of the directrix. Then ske

1. **Problem Statement:** Given the parabola equation $y^2 = 8x$, find the coordinates of the focus, the endpoints of the latus rectum, and the equation of the directrix. Then sket

1. **State the problem:** Transform the equation $$2x^2 + 2y^2 + 9x - 4y - 60 = 0$$ into the center-radius form of a circle. 2. **Rewrite the equation:** Divide the entire equation

1. **State the problem:** Find the general form of the equation of the circle with diameter endpoints at (5, -6) and (-3, -6). 2. **Formula and rules:** The general form of a circl

1. **State the problem:** Factor the expression $x^2$. 2. **Understand the expression:** $x^2$ means $x$ multiplied by itself: $x \times x$.

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

1. **State the problem:** Simplify and add the expressions $$\frac{16x^2 - 8x + 1}{9x} + \frac{12x + 3}{1 - 16x^2}$$. 2. **Identify the formula and rules:** To add fractions, find

1. The problem involves evaluating the expression $5x^3 - 3x^2 - 2(x - 10)^2$ at $x = -2$ and understanding the calculation steps. 2. The formula used is substitution into the poly

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

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

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

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

1. The problem is to factor the expression $x^2 - 4$. 2. Recognize that this is a difference of squares, which follows the formula $a^2 - b^2 = (a - b)(a + b)$.

1. The problem is to analyze the function $x^2 - 4$. 2. This is a quadratic function in the form $f(x) = ax^2 + bx + c$ where $a=1$, $b=0$, and $c=-4$.

1. The problem is to analyze the function $x^2 - 4$. 2. This is a quadratic function in the form $f(x) = ax^2 + bx + c$ where $a=1$, $b=0$, and $c=-4$.

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule:

1. **State the problem:** Factor the expression $x^2$. 2. **Recall the factoring rules:**

1. **State the problem:** Calculate $$\frac{13!}{720} - 89^3 + \sqrt{473926185} - 18294637$$. 2. **Recall factorial and exponentiation:**

1. **State the problem:** Calculate the value of $$73^5 + \sqrt{987654321} - \frac{293847 \times 476}{1829} + 37^4$$. 2. **Recall formulas and rules:**

1. We are given the system of equations: $$3x + 8y = 12 \quad (1)$$