🧮 algebra

1. **State the problem:** Expand the expression $ (xy)^3 $. 2. **Formula used:** The power of a product rule states that $ (ab)^n = a^n b^n $.

1. The problem is to expand $(-5)^3$. 2. The expression $(-5)^3$ means multiplying $-5$ by itself three times.

1. The problem asks to find the unit rate from the graph "Cost of Coffee" which shows cost in dollars versus number of pounds. 2. The formula for unit rate is $$\text{Unit Rate} =

1. Énonçons le problème : Montrer que pour tout entier naturel $n$, on a $u_{n+1} - u_n = 5 \times 0,8^n$ et en déduire le sens de variation de la suite $(u_n)$.\n\n2. Rappelons qu

1. The problem states that the function $f$ is defined by $f(x) = 7x^3$ and the graph of $y = g(x)$ is obtained by shifting the graph of $y = f(x)$ down 2 units. 2. When a graph is

1. **State the problem:** Simplify the expression $$\frac{3(t + h)^2 - 3}{h}$$ and find its simplified form. 2. **Recall the formula and rules:** We will expand the square, simplif

1. **State the problem:** Devi wants to rent a car from Company A or Company B. Company A charges 45 per day, Company B charges 38 per day plus a fixed 75 charge. We want to find w

1. **State the problem:** We want to find the value of $c$ such that the parabola $y = -x^2 + 9x - 100$ intersects the line $y = c$ at exactly one point. 2. **Understand the condit

1. Stating the problem: Calculate 8.5% of 620. 2. Formula: To find a percentage of a number, use the formula $$\text{Percentage value} = \frac{\text{percentage}}{100} \times \text{

1. **State the problem:** We want to find which expression is equivalent to $$6x^8 y^2 + 12x^2 y^2$$.

1. **Stating the problem:** Siti has 50 pieces of $5-notes and $2-notes in total. Let $y$ be the number of $5-notes. Then the number of $2-notes is $50 - y$. The total value of all

1. **State the problem:** Solve the quadratic equation $$z^2 + 10z - 24 = 0$$ to find the values of $z$. 2. **Recall the quadratic formula:** For an equation $$az^2 + bz + c = 0$$,

1. **State the problem:** Simplify or evaluate the expression $2a + 5b - 4$ if values for $a$ and $b$ are given, or understand its structure as an algebraic expression. 2. **Unders

1. The problem is to evaluate the expression $3^{-2} + 6^{-1}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$.

1. **State the problem:** Solve the equation $4x - 8 + 5 = 1 - 3x - 9 + 12x$ for $x$. 2. **Simplify both sides:**

1. **State the problem:** Find the product of the binomials $$(7m + 8n)(7m - 8n)$$. 2. **Recall the formula:** This is a difference of squares pattern, which states:

1. The problem asks for the number of values of $x$ such that $f(x) = 0$ where $f(x) = ax^3 + bx^2 + cx + d$ is a cubic function. 2. A cubic function can have up to 3 real roots be

1. **State the problem:** Jordan uses 24 pints of paint in total. One quarter ($\frac{1}{4}$) of this paint is green, and the rest is blue. We need to find how many pints of blue p

1. **Stel het probleem vast:** We willen weten hoeveel kilogram suiker er in de voorraadpot zit als deze tot 3 cm onder de rand gevuld is.

1. **State the problem:** In the library, the number of fiction books is $\frac{2}{5}$ the number of nonfiction books. The total number of books is 56. We need to find how many boo

1. Problema: Simplificar la expresión $ (2x)^3 $ usando las leyes de exponentes. 2. Fórmula: Para un producto elevado a una potencia, se eleva cada factor a esa potencia: $$ (ab)^n