🧮 algebra

1. **Énoncé du problème :** Calculer les expressions algébriques données avec les binômes $A = x + 2$, $B = x + 7$, $C = x^2 - 3$, $D = 3x + 1$.

1. **State the problem:** Simplify the expression $$(b x^4 - 3 b^2 x^3 + 4 b^4 x - b)(-2 b^3 x^2).$$ 2. **Recall the distributive property:** To multiply a polynomial by a monomial

1. The problem asks to determine the number of solutions (0, 1, or infinite) for each given equation after substitution or elimination in a system. 2. Important rules:

1. The problem is to simplify the expression $\left(\right)dee$, which appears to be incomplete or incorrectly formatted. 2. Normally, parentheses enclose terms or expressions, but

1. We hebben de functie gegeven als $$P(t) = 7 \cdot 0{,}962^{t+1}$$ waarbij $t$ de tijd in dagen is en $P(t)$ de druk in bar. 2. Het probleem vraagt naar de waarde waar de druk ui

1. El problema es calcular la variable $Z$. 2. Primero, necesitamos saber la fórmula o contexto donde aparece $Z$ para poder calcularlo.

1. **State the problem:** We need to draw the graph of the linear function $y = 3x - 4$ on a Cartesian coordinate plane. 2. **Formula and explanation:** The function is given by th

1. **State the problem:** Write the logarithm \( \log \left( \frac{m^4 + n}{100} \right) \) as a difference of logarithms using the quotient property. 2. **Recall the quotient prop

1. **State the problem:** We need to find the expression that represents the perimeter of Humberto's backyard, which is a rectangle with length $x + 6$ and width $2x - 1$. 2. **Rec

1. **State the problem:** Simplify the expression $ (2x - 4) - (3x + 2) $. 2. **Write the expression:**

1. **State the problem:** We are given the graph of a function $f$ which is a straight line passing through points approximately $(-1, 3)$ and $(1, -1)$. We need to find: (a) One v

1. **State the problem:** Simplify the expression $$\frac{2 \left( \frac{4}{2-x} \right) - 4}{x}$$. 2. **Rewrite the numerator:** Multiply inside the parentheses:

1. **State the problem:** We are given a sequence with terms $a_1=2$, $a_2=4$, $a_3=8$, $a_4=16$, $a_5=32$, $a_6=64$. We want to find which function rule represents this sequence.

1. Het probleem is om de uitdrukking $a^2 - b^2$ te begrijpen en te vereenvoudigen. 2. We gebruiken de formule voor het verschil van kwadraten: $$a^2 - b^2 = (a - b)(a + b)$$

1. Planteamos el problema: Dividir el polinomio $3x - 2x^2 - x^4 + 5$ entre $x^2 + 2x - 3$. 2. Ordenamos los polinomios de mayor a menor grado:

1. **State the problem:** We have a parabola with vertex at $(9, -14)$ and two x-intercepts. The parabola's equation is $y = ax^2 + bx + c$. We need to find which value among $a+b+

1. **State the problem:** Solve the equation $$18 = \frac{a}{3} - 12$$ for the variable $a$. 2. **Add 12 to both sides** to isolate the term with $a$:

1. **State the problem:** Find the perpendicular distance from the point $P(5, -2)$ to the line given by the equation $$y = \frac{4}{3}x - 11.$$ 2. **Formula used:** The distance $

1. **Problemstellung:** Gegeben sind die Funktionen: $$f(x) = -2 \cdot 4^x, \quad g(x) = 1{,}5 \cdot 6^x, \quad h(x) = -4 \cdot 0{,}5^x, \quad k(x) = 4 \cdot 2^x$$

1. **State the problem:** Solve the equation $-36a^2 = 8a$ for $a$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. The problem asks to express $\left(\frac{y}{2}\right)^{-4}$ in the form $a y^n$ where $a$ and $n$ are integers. 2. Recall the rule for negative exponents: $x^{-m} = \frac{1}{x^m