🧮 algebra

1. **Problem statement:** Factorise the quadratic expression $$6x^2 + 11xy + 5y^2$$. 2. **Formula and approach:** To factorise a quadratic expression of the form $$ax^2 + bxy + cy^

1. **State the problem:** Find the equation of the line of intersection between the planes given by $$x + 5y - z = 20$$

1. **State the problem:** Simplify the expression $$5 \cdot (25)^{n+1} - 25 \cdot 5^{2n}$$. 2. **Recall the rules:**

1. Das Thema ist quadratische Funktionen. Eine quadratische Funktion hat die allgemeine Form $$f(x) = ax^2 + bx + c$$, wobei $$a \neq 0$$ ist. 2. Wichtige Eigenschaften sind:

1. **State the problem:** Solve the equation $4x^2 - 5(x - 2) = 10$ for $x$. 2. **Expand and simplify:** Distribute the $-5$ across $(x - 2)$:

1. **State the problem:** Solve the quadratic equation $$3x^2 + 5(2x + \frac{5}{3}) = 0$$. 2. **Expand the equation:** Use the distributive property to expand the term $$5(2x + \fr

1. **State the problem:** Solve the linear equation $2x - 7 = 0$ for $x$. 2. **Write the equation:**

1. We are asked to solve the equation $3^x = 27^x$ using logarithms. 2. First, recognize that $27$ can be written as a power of $3$: $27 = 3^3$.

1. We are asked to explain step 15 better. Since the original problem or context is not provided, let's assume step 15 involves simplifying or solving an algebraic expression. 2. G

1. **State the problem:** Simplify the expression $$\left( \frac{x^{5}y^{-3}}{2xy^{5}} \right)^{-4} \div \frac{4x^{6}y^{-10}}{\left( 3x^{-2}y^{2} \right)^{-3}}.$$\n\n2. **Simplify

1. **State the problem:** Simplify the expression $$\left(\frac{x^{5} y^{-3}}{2x y^{5}}\right)^{-4} \div \frac{4x^{6} y^{-10}}{\left(3x^{-2} y^{2}\right)^{-3}}.$$\n\n2. **Rewrite t

1. **State the problem:** Simplify the expression $$\left(\frac{x^{5} y^{-3}}{2x y^{5}}\right)^{-4} \div \frac{4x^{6} y^{-10}}{\left(3x^{-2} y^{2}\right)^{-3}}.$$\n\n2. **Rewrite t

1. **Aufgabe 6: Terme vereinfachen** **a)** $(a + 9)^2$

1. Problem: Vereinfache den Term a) (a + 9)^2 mithilfe der binomischen Formel. 2. Formel: Die erste binomische Formel lautet $$ (x + y)^2 = x^2 + 2xy + y^2 $$.

1. Aufgabe: Vereinfache die Terme mithilfe der binomischen Formeln und dem Ausmultiplizieren von Summen. 2. Wichtige Formeln und Regeln:

1. The problem is to solve for $z$ in the equation $z \div 7 = 8$. 2. The division equation can be rewritten as a multiplication equation using the property that dividing by a numb

1. Stating the problem: Solve for $m$ in the equation $m \div 9 = 6$. 2. Use the division equation rule: To isolate $m$, multiply both sides of the equation by 9.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{75a^5}}{\sqrt{3a}}$$. 2. **Use the property of radicals:** $$\frac{\sqrt{x}}{\sqrt{y}} = \sqrt{\frac{x}{y}}$$.

1. Das Problem lautet: Vereinfachen Sie den Ausdruck $$c^{\frac{1}{2}} \div c^3$$. 2. Die Regel für Division von Potenzen mit gleicher Basis lautet: $$a^m \div a^n = a^{m-n}$$.

1. Stating the problem: Convert 4,800 into scientific notation in the form $a \times 10^b$ where $1 \leq a < 10$ and $b$ is an integer. 2. Scientific notation rule: Move the decima

1. **State the problem:** We need to find how much larger Wisconsin is compared to South Carolina by subtracting the area of South Carolina from Wisconsin's area. 2. **Write down t