🧮 algebra

1. **State the problem:** Simplify the expression $a(a^2 + ab + b^2) - b(a^2 + ab + b^2)$.\n\n2. **Identify the common factor:** Notice that both terms share the common factor $(a^

1. The problem is to understand and simplify surds, which are irrational numbers expressed with roots, such as square roots. 2. The key formula to remember is that $$\sqrt{a} \time

1. **State the problem:** Simplify the expression $3 \sqrt{18} \times 5 \sqrt{2}$. 2. **Recall the properties of square roots:**

1. **State the problem:** We are given that a 15% discount equals 180, and we need to find the marked price (MP). 2. **Formula and explanation:** The discount is calculated as a pe

1. **Problem statement:** સપનાએ ₹20,800 સદા વ્યાજ પર અંશત: વાર્ષિક 11% દરે અને અંશત: વાર્ષિક 9% દરે રોકાણ કર્યા છે. 6 વર્ષ પછી બંને રોકાણોમાંથી સમાન વ્યાજ મળે છે. 11% દરે રોકાણ કરે

1. The problem is to continue with the operations, but since no specific operations were given, let's assume we are continuing a general algebraic operation. 2. Suppose we have an

1. **Problem Statement:** Show that if a line passes through points $(x_1, y_1)$ and $(h, k)$ with slope $m$, then the equation $k - y_1 = m (h - x_1)$ holds.

1. **State the problem:** We are given two equations:

1. **Problem statement:** We are given two lines where the slope of one line is double the slope of the other. The tangent of the angle between these two lines is $\frac{1}{3}$. We

1. **State the problem:** Solve the system of equations:

1. **State the problem:** Solve the system of linear equations:

1. **State the problem:** Solve the system of equations by elimination: $$13x + 48 = 8y$$

1. The problem is to find the sequence pattern in the given multipliers: 1.06x, 4.35x, 8.83x, 259.21x, 1.48x, 1.26x, 12.29x, 1.69x, 1.25x, 4.95x, 1.00x, 1.49x, 2.80x, 1.86x, 1.22x,

1. Vamos a resolver una ecuación cuadrática más difícil: $$2x^2 - 7x + 3 = 0$$. 2. La fórmula para resolver ecuaciones cuadráticas es la fórmula cuadrática:

1. **State the problem:** Simplify the expression $-0.12 \div 13$. 2. **Formula and rules:** Division of decimals by whole numbers can be done by dividing the decimal number direct

1. El problema es practicar la racionalización de expresiones algebraicas que contienen raíces en el denominador. 2. La racionalización consiste en eliminar raíces del denominador

1. The problem asks to find the sum of all sums and provide formulas. 2. To clarify, the sum of a sequence of numbers can be found using different formulas depending on the type of

1. **State the problem:** Find the rectangular and inclined asymptotes of the curve defined by the equation $ (x + y)^2 (x + 2y + 2) = (x + 9y - 2) $. 2. **Rewrite the equation:**

1. **State the problem:** Calculate the value of the expression $(14-16.58)+5(15-16.58)+3(16-16.58)+2(17-16.58)+2(18-16.58)+(25-16.58)$. 2. **Rewrite the expression:** Note that co

1. El problema es practicar la racionalización en álgebra, que consiste en eliminar raíces del denominador de una fracción. 2. La fórmula básica para racionalizar un denominador co

1. Planteamos el problema: Resolver el sistema de ecuaciones $$\begin{cases} 3x - \frac{y - 3}{5} = 6 \\ 3y - \frac{x - 2}{7} = 9 \end{cases}$$