🧮 algebra

1. **State the problem:** Factor the expression $4ab^2 - 36a$ completely. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $4a$ because $4$ divides bot

1. **State the problem:** We want to prove that the expression $$8 - x^2 + 3x - 9 + 5(x - 1) - x(6 - 5) = 0$$ for all values of $x$. 2. **Write down the expression clearly:**

1. Problemet handler om at finde sammenhængen mellem hestens stangmål i meter og det mindste areal, som opstår ved at gange stangmålet med sig selv og med 2,89. 2. Formlen for mind

1. The problem asks to write the fraction $\frac{5}{6}$ as a whole number. 2. A fraction represents a part of a whole. To write a fraction as a whole number, the numerator must be

1. **Stating the problem:** We have a scatter plot showing the number of calls $n$ Pete made each month and the corresponding cost $b$ in dollars. We need to find the equation of t

1. The problem is to understand how multiplying an equation by 60 removes denominators. 2. Suppose you have an equation with fractions, for example: $$\frac{a}{b} + \frac{c}{d} = e

1. **State the problem:** Matthew rides for $x$ km at 12 km/h. Zoe rides for $x+4$ km at 10 km/h. Their total riding time is 1.5 hours. We need to find $x$ and $x+4$. 2. **Formula:

1. The problem is to simplify expressions using index laws. 2. Index laws (or laws of exponents) include:

1. **State the problem:** Simplify the expression $ (6 \times 5)^2 $. 2. **Recall the formula:** When you have a product inside parentheses raised to a power, use the rule $ (ab)^n

1. **State the problem:** Simplify the expression $\sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5}$ and express it in the form $5^y$. 2. **Recall the formula and rules:** Addi

1. **Stating the problem:** We are given $x = 2 \times 10^{5}$ and $y = 3 \times 10^{-3}$, each correct to one significant figure. We need to find the greatest and least possible v

1. **State the problem:** Solve the equation $$6^x = \frac{12^x}{8}$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by 8 to eliminate the denominator:

1. **State the problem:** Solve the equation $$4^{2x} = 8^{1-x}$$ for $x$. 2. **Rewrite bases as powers of 2:**

1. **State the problem:** Solve the exponential equation $$32^{2x - 1} = \frac{1}{8}$$. 2. **Rewrite bases as powers of 2:**

1. **State the problem:** Solve the equation $4^{x - 3} = 256$ for $x$. 2. **Recall the formula and rules:** We know that $4^{x - 3}$ means $4$ raised to the power of $(x - 3)$. To

1. **Problem statement:** We are given two linear equations: $$y = 4 - x$$

1. **Problem statement:** Factorise $a^4 + 4b^4$ by adding and subtracting $4a^2 b^2$.

1. **Problem statement:** Given the linear equation $y = 5x - 4$, we need to find: (a) The value of $x$ when $y=0$.

1. **State the problem:** Solve the equation $$\frac{3}{4}(x - 7) = 9$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. Thi

1. **State the problem:** Solve the quadratic equation $x^2 - 7x - 34 = 10$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** We need to find the total cost to buy carpet to cover the floor of a square-shaped room with side length 4 metres, where the carpet costs 99 per square me