🧮 algebra

1. **State the problem:** Simplify the expression $3x + 2x$. 2. **Recall the rule:** When adding like terms, add their coefficients and keep the variable the same.

1. The problem is to simplify the expression $3x + 2x$ using the terms $1, -1, x, -x, x^2, -x^2$. 2. The formula for combining like terms is to add or subtract the coefficients of

1. **State the problem:** Solve the equation $15x + 5 = -1$ for $x$. 2. **Write down the equation:**

1. The problem is to evaluate the expression $x^2 + 5x$ for $x = -2$. 2. The formula given is a quadratic expression: $x^2 + 5x$.

1. The problem asks to identify the algebraic transformation that maps the first square with vertices \((-4,7), (-1,7), (-1,4), (-4,4)\) to the second square with vertices \((2,3),

1. The problem is to simplify the expression $\frac{1}{2} \div 3 \div 4$. 2. Division of fractions and numbers can be handled by converting division into multiplication by the reci

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