🧮 algebra

1. **State the problem:** Factor the quadratic expression $x^2 + 9x + 18$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multip

1. The problem states: "5 times a number D". We need to express this phrase as a mathematical expression. 2. The phrase "times a number" means multiplication. So, "5 times a number

1. The problem asks for "5 times a number d." This means we want to express the product of 5 and the variable $d$. 2. The formula for multiplying a number by a variable is simply t

1. Problem Q1: Given $f(x) = \frac{(1 + 2x)^2}{(1 - x)^2}$ (i) Find the first 4 terms in the power series expansion.

1. **State the problem:** We are given the linear equation $y = 2x + 3$ and asked to find the value of $y$ when $x = 2$. 2. **Formula used:** The equation is already given in slope

1. Problem 1: Given $f(x) = \frac{(1+2x)^2}{1-x^2}$ (i) Find the first 4 terms in the power series expansion.

1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n}$$ and find its value when $$n = 10$$. 2. **Write the expression:** The expression is $$\frac{n^2 + n}{n

1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n}$$ and find its value when $$n = 10$$. 2. **Write the expression:** $$\frac{n \times n + n}{n}$$.

1. **State the problem:** Simplify the expression $x + x + 2$. 2. **Formula and rules:** When adding like terms, add their coefficients. Here, $x$ and $x$ are like terms.

1. **State the problem:** We need to find which of the given equations have no solution. 2. **Recall:** An equation has no solution if, after simplification, it results in a contra

1. **State the problem:** Determine if each equation is true for one value, all values, or no values of $x$. 2. **Equation 1:** $10 + 3x = -4.2x + 9$

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. **State the problem:** Luke has red and blue marbles. Initially, the probability of choosing a blue marble is $\frac{2}{5}$. After adding 5 blue marbles and removing 5 red marbl

1. Let's start by defining the terms. 2. The **domain** of a function is the set of all possible input values (usually $x$ values) for which the function is defined.

1. **State the problem:** Find the range of the function $$f(x) = x^3 - 27$$. 2. **Recall the formula and properties:** The function is a cubic polynomial. Cubic functions of the f

1. **State the problem:** Solve the quadratic equation $ax^2 + bx + c = 0$ using the quadratic formula. 2. **Formula:** The quadratic formula is given by

1. Stating the problem: We want to check if the equation $b \times b \times b = b + b + b$ is true. 2. Understanding the equation: The left side is $b$ multiplied by itself three t

1. **State the problem:** Simplify the expression $x + x$. 2. **Formula and rules:** When adding like terms, you add their coefficients. Here, both terms are $x$, which means the c

1. **State the problem:** Solve the equation $b \times b \times b = b + b + b$ for $b$. 2. **Rewrite the equation:** The left side is $b^3$ and the right side is $3b$, so the equat

1. **State the problem:** Solve the equation $b \times b \times b = b + b + b$. 2. **Rewrite the equation:** The left side is $b^3$ and the right side is $3b$, so the equation beco

1. **State the problem:** Solve the equation $b \times b \times b = b + b + b$. 2. **Rewrite the equation:** The left side is $b^3$ and the right side is $3b$, so the equation beco