🧮 algebra

1. **State the problem:** Simplify the expression $$2ab^2 - [(a+b)(a-b) - ab(a - 2ab)]a^2b$$. 2. **Recall formulas and rules:**

1. The problem asks to find the reciprocal of 0.625. 2. The reciprocal of a number $x$ is given by the formula $$\text{reciprocal} = \frac{1}{x}$$.

1. **State the problem:** We have a right-angled triangle with legs $6x$ cm and $8$ cm, and a rectangle with sides $5$ cm and $4x - 1$ cm.

1. **State the problem:** We are given two equations involving $a$, $b$, and their product $ab$: $$\frac{ab}{3a + 2b} = \frac{1}{5}$$

1. **State the problem:** We have a geometric series given by $$4(3p - 1) + 2x(3p - 1)^2 + \ldots$$ and we want to determine the values of $$x$$ for which this series converges. 2.

1. **Stating the problem:** We are given two lines:

1. **State the problem:** Solve the equation $$11 - 3 \sqrt{28} x = 52$$ for $x$. 2. **Isolate the term with $x$:** Subtract 11 from both sides:

1. **State the problem:** We are given a rectangle with length $x^2 + 8x + 15$ and width $x + 3$. We need to find the length in meters, which is the expression for the length side.

1. **State the problem:** Factor the quadratic expression $$x^2 - 3x - 10$$ as the product of two binomials. 2. **Recall the factoring formula:** For a quadratic in the form $$x^2

1. **Énoncé du problème** : Calculer les trois premiers termes de la suite $u_n = -2n^2 + 20n + 4$ pour $n \in \mathbb{N}$, puis déterminer ses variations. 2. **Formule et règles i

1. The problem is to understand the general form of the equation of a straight line and the meaning of its components. 2. The general form of the equation of a straight line is $$y

1. El problema consiste en simplificar la expresión $$-2x^3y^4 - 25x^3y^4 - 6x^3y^4$$ mediante la reducción de términos semejantes. 2. Los términos semejantes son aquellos que tien

1. **State the problem:** Simplify the expression $$2(x-5)^2 + 4(x-5) + 4$$ into a polynomial in standard form. 2. **Recall the formula:** The square of a binomial is given by $$ (

1. **State the problem:** Expand and express the product \((2x+5)(x+10)\) as a trinomial. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: \((a+b)(c+

1. **State the problem:** We are given a system of equations involving dimes ($x$) and quarters ($y$): $$0.10x + 0.25y = 3.65$$

1. **State the problem:** Josie wants to make lemonade servings using the recipe amounts: syrup 3/4 oz, lemon juice 2 1/4 oz, and water 5 oz per serving. She has 20 oz syrup, 33 oz

1. **State the problem:** We need to analyze and understand the function $f(x) = \sqrt{x} - 3$. 2. **Recall the domain of the square root function:** The expression inside the squa

1. **State the problem:** We have a building with 26 apartments of sizes 90, 120, 140, and 150 m². The number of 120 m² apartments is $x$, and the number of 90 m² apartments is unk

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. **Problem 7:** Find the slope-intercept form of the line graphed on the coordinate plane. 2. **Step 1: Identify two points on the line.**

1. **Problem:** Factorize the expression $9x^2 + 8x - 1$. 2. **Formula and rules:** To factorize a quadratic expression $ax^2 + bx + c$, we look for two numbers that multiply to $a