🧮 algebra

1. **Problem 1: Solve the system of equations:** $$x^2 + y^2 = 25$$

1. **State the problem:** Solve the equation $5x + 2 = 7x$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate $x$ by moving all terms with $x$

1. **State the problem:** We want to understand how the terms 27 and -10 appeared in the equation after multiplying both sides by the common denominator $ (x-3)(x+3) $. 2. **Recall

1. Stating the problem: Given $a = 2^5 + 2^{-5}$ and $b = 2^5 - 2^{-5}$, find $a^2 - b^2$. 2. Recall the identity: $$a^2 - b^2 = (a-b)(a+b)$$

1. **Stating the problem:** We need to find the solution regions (daerah yang memenuhi) for the inequalities:

1. The problem is to simplify the expression $\sqrt[4]{25x^4}$.\n\n2. Recall the rule for fourth roots: $\sqrt[4]{a^4} = a$ if $a \geq 0$. Also, $\sqrt[4]{ab} = \sqrt[4]{a} \times

1. The problem is to simplify the expression $\sqrt[25]{x^4}$.\n\n2. The general rule for radicals is $\sqrt[n]{a^m} = a^{\frac{m}{n}}$. This means the $n$th root of $a$ to the pow

1. The problem is to calculate the value of $\frac{1}{25} \times 4$. 2. The formula for multiplication of fractions is $\frac{a}{b} \times c = \frac{a \times c}{b}$.

1. The problem is to simplify the expression $\sqrt{25x^2}$.\n\n2. Recall the property of square roots: $\sqrt{a^2} = |a|$, which means the square root of a square is the absolute

1. **State the problem:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Recall the formula:** For a quadratic equation $$ax^2 + bx + c = 0$$, the solutions can be found u

1. **State the problem:** Simplify or factor the quadratic expression $x^2 + 7x + 12$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. **State the problem:** Simplify or factor the quadratic expression $x^2 + 3x + 2$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. **Problem:** Add $\frac{1}{2} + \frac{1}{4}$. 2. **Formula:** To add fractions, first find a common denominator, then add the numerators.

1. Problem: Add $\frac{1}{2} + \frac{1}{4}$. 2. Formula: To add fractions, use $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \neq 0$.

1. Nyatakan masalah: Sederhanakan $49 \times 27 \times 7^5$.\n 2. Rumus dan aturan penting: bila basis sama gunakan $a^m \times a^n = a^{m+n}$.\n

1. State the problem: Simplify the expression $4x^2 - 7x^2 + 3x - 5x^3$. 2. Formula and rules: To combine like terms use $ax^n + bx^n = (a+b)x^n$.

1. **State the problem:** Simplify the expression $-\frac{62}{6} + 4 + \frac{32}{3} + 8$. 2. **Find a common denominator:** The denominators are 6 and 3. The least common denominat

1. **Calculer les expressions données :** a. Calculer $A = \sqrt{4^2} + 3^5$

1. **State the problem:** Simplify or factor the expression $x^2 - 30x + 225$. 2. **Recall the formula:** To factor a quadratic expression of the form $ax^2 + bx + c$, we look for

1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 34x + 289$. 2. **Recall the formula:** To factor a quadratic expression of the form $ax^2 + bx + c$, we

1. **مقارنة العددين** $7\sqrt{2}$ و $5\sqrt{3}$. 2. نبدأ بحساب قيم كل عدد تقريبا: