🧮 algebra

1. **State the problem:** Simplify the expression $$(4b - 1)(3b - 7)$$. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term

1. **Énoncé du problème :** Calculer $P(3)$ pour le polynôme $$P(x) = x^3 - (4 + \sqrt{3})x^2 + (3 + 4\sqrt{3})x - 3\sqrt{3}.$$ 2. **Formule utilisée :** Pour calculer $P(3)$, on r

1. **State the problem:** Simplify the expression $$(5x^3 - 6x + 10) + (x^3 + 10x - 9)$$. 2. **Combine like terms:** Group the terms with the same powers of $x$ together.

1. **State the problem:** Simplify the expression $3\sqrt{48} - \sqrt{12}$. 2. **Recall the rule:** $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and simplify square roots by fact

1. **State the problem:** Multiply the expressions $(-7x^2 + 9x - 15)$ and $(8x - 8)$. 2. **Formula and rules:** To multiply two polynomials, use the distributive property: multipl

1. **State the problem:** Solve the system of equations $$\begin{cases} x + 3y = 6 \\ x = 2 + y \end{cases}$$

1. **State the problem:** We are given the ellipse equation $$\frac{(x-1)^2}{9} + \frac{(y+4)^2}{16} = 1$$ and need to find the center, major and minor axes with their lengths, ver

1. **State the problem:** We need to analyze the function $$y=\sqrt{5x^2+1}$$. 2. **Formula and rules:** The function is a square root of a quadratic expression. The square root fu

1. **Problem 6:** Solve the system using substitution or elimination method. Given:

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{x} + 4! + \sqrt{x} = 12.$$\n\n2. **Recall the factorial value:** $4! = 4 \times 3 \times 2 \times 1 = 24$.\n\n3. **R

1. Problem: Add the polynomials \((4x^2 + 4x + 1) + (4x + 20)\). 2. Formula: To add polynomials, combine like terms (terms with the same power of \(x\)).

1. **State the problem:** Given the equation $x^2 = 623 - \frac{1}{x^3}$, find the value of $x^3 + \frac{1}{x^3}$.\n\n2. **Rewrite the given equation:** Multiply both sides by $x^3

1. The problem is to solve the equation $$\frac{2x+3}{x-1} = 4.$$\n\n2. The formula used here is to solve rational equations by eliminating the denominator: multiply both sides by

1. **State the problem:** Rewrite the hyperbola equation $$9x^2 - 4y^2 - 36x - 40y - 388 = 0$$ in standard form and find its center, foci, vertices, and asymptotes.

1. **State the problem:** We need to find and combine like terms in each expression. 2. **Recall the rule:** Like terms have the same variable(s) raised to the same power.

1. **State the problem:** Simplify the expression $$\frac{2}{4r+3} \times \frac{28r+21}{r}$$. 2. **Rewrite the expression:**

1. **State the problem:** Simplify the expression $$\frac{8k^2 + 2k}{7(4k + 1)}$$. 2. **Factor the numerator:** Factor out the common factor $2k$ from the numerator:

1. **State the problem:** We are given two linear equations: $$y = 5 + 6x$$

1. **State the problem:** We need to find a two-digit number whose digits sum to 8 and when the digits are interchanged, the new number is 36 greater than the original. 2. **Define

1. The problem is to find the values of $a$, $b$, and $k$ in the exponential function $f(x) = a b^x + k$ given the table of values: $$\begin{array}{c|ccccc} x & 0 & 1 & 2 & 3 & 4 \

1. **State the problem:** Simplify the expression $$(5a^2 - 6 + 9)(2a - 3) - (2a^2 - 5a + 4)(5a + 1).$$ 2. **Rewrite and simplify inside parentheses:**