🧮 algebra

1. نبدأ بكتابة مسألة السؤال: لدينا دالة د معرفة على مجال ح ونعلم أن $$3d(x) + d(-x) = x^4 - 2x^2 + 1$$

1. **State the problem:** Simplify the expression $$2x^2(5x^5)$$. 2. **Apply the multiplication rule for exponents:** Multiply the coefficients and add the exponents of like bases.

1. Simplify each expression by distributing and combining like terms. 16. Simplify $2(x^2 + 2) + 3(2x + 3)$:

1. Soddalashtiring: 1) $x^2 + 3x + 2 + (2x^2 - 3x + 2)$

1. The problem presents the inequality $31 > 28$. 2. We need to verify if 31 is indeed greater than 28.

1. Evaluate $2^{-4}$. Recall that $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** We have three lengths of wood in the ratio $2 : 5 : 7$. The difference between two of them is 30 cm. We want to verify if Kofi's statement that the sum of

1. *مقدمة: تعريف الأعداد النسبية* الأعداد النسبية هي الأعداد التي يمكن كتابتها على شكل \(\frac{a}{b}\) حيث \(a\) و \(b\) عددان صحيحان و \(b \neq 0\).

1. Problem 16: A student scores 10 out of 15 on Part 1 and 4 out of 10 on Part 2. To pass the exam, the student needs at least 54% of the total marks. 2. Calculate total marks obta

1. The problem is to express the fraction \(\frac{1}{2}\) in a clear way. 2. \(\frac{1}{2}\) means one part out of two equal parts.

1. Stating the problem: Simplify the expression $$\frac{(9 \times 3^2)^3}{(3 \times 27)^2}$$. 2. Simplify inside the parentheses.

1. Let's start with the first expression: \(2^7 \times 2^4 \times 2^{-8}\). 2. When multiplying powers with the same base, add the exponents:

1. **Problem (a):** Sundip buys 30 litres of fuel at £1.50 per litre and pays the exact amount using three bank notes of £5, £10, £20, or £50. 2. Calculate the total cost of fuel:

**Problem:** Write Leo's time as a fraction of Eve's time and simplify the fraction.

1. **Stating the problem:** We have a sequence of terms $T_1, T_2, \\ldots, T_6$ given as $0, 4, 8, 12, 0, 16$ respectively. 2. We need to find the smallest index $k$ such that $T_

1. Problem (a): Simplify the expression $4x - 3y + x + 7y$. Step 1: Group like terms.

1. We start with Bottle A containing 1.5 litres of water and Bottle B containing 100 millilitres of water. 2. Convert 1.5 litres to millilitres because we need to work in the same

1. **Stating the problem:** We want to calculate the product of the fraction $\frac{2}{7}$ multiplied by $-28$. 2. **Rewrite the expression:** The problem is

1. Énonçons le problème : développer et réduire l'expression $$ (5\sqrt{5} - 4)(5\sqrt{5} - (-4)) $$. 2. Simplifions l'expression dans la deuxième parenthèse : $$ 5\sqrt{5} - (-4)

1. We are asked to simplify the expression $$\frac{+36}{+6}$$. 2. Both numerator and denominator have a positive sign, which means the fraction is positive.

1. Le problème est de simplifier la racine carrée de la fraction $\frac{49}{49}$. 2. On utilise la propriété que $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ pour $a,b > 0$.