🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{x^2 - 1}{x(x + 2)} \times y \times \frac{3x}{x^2 + 2x}$$. 2. **Recall important formulas and rules:**

1. **State the problem:** Simplify the expression $$\left(-\frac{1}{2}\right)-1$$. 2. **Recall the rule:** Subtracting a number is the same as adding its negative. So, $$a - b = a

1. The problem asks whether substituting a variable $u$ and then replacing it back with $y$ is common practice or bad notation. 2. In mathematics, substitution is a technique used

1. **Problem statement:** We are given two inequalities:

1. **State the problem:** We have a rectangle with width $x$ cm and length $4x + 1$ cm.

1. **State the problem:** We need to find the factorization of the expression $$a^3 - b^3$$. 2. **Formula used:** The difference of cubes formula is:

1. The problem is to understand the expression $x^2$. 2. The expression $x^2$ means $x$ multiplied by itself, which is called "x squared".

1. The problem is to understand the expression $\sqrt{x}$, which represents the square root of $x$. 2. The square root of a number $x$ is a value that, when multiplied by itself, g

1. **Problem 1: Add polynomials by combining like terms.** Given: $$(2x^3 - 3x^2 + 4x) + (-3x^3 + 5x^2 - 2x)$$

1. The problem is to understand how to use absolute value in inequalities. 2. The absolute value of a number $x$, denoted $|x|$, is the distance of $x$ from zero on the number line

1. **State the problem:** Solve the inequality $$3|10m+4|-1 \geq 41$$. 2. **Isolate the absolute value:** Add 1 to both sides:

1. **Stating the problem:** We want to understand how to multiply and divide fractions. 2. **Multiplication of fractions formula:** To multiply two fractions $$\frac{a}{b}$$ and $$

1. The problem asks us to compare two expressions: $N^{1.1}$ and $100^N$. 2. We want to determine which is larger for a given value of $N$.

1. **Problem:** Given $f(x) = x^2 + 2$ and $(f \circ g)(x) = 9x^2 - 6x + 3$, find $g(x)$. 2. **Formula and rules:** The composition $(f \circ g)(x) = f(g(x))$. Since $f(x) = x^2 +

1. **State the problem:** Solve the inequality $$2x^2 + 3x - 2 < 0$$. 2. **Formula and rules:** To solve quadratic inequalities, first find the roots of the quadratic equation $$2x

1. **State the problem:** We want to find the sign of the function $$f(x) = (2x - 1)(3x + 5)(x + 1)$$ on the interval $$-\frac{5}{3} < x < \frac{1}{2}$$ given that the zeros are at

1. **State the problem:** We want to determine the sign of the function $$f(x) = (5x + 1)(4x - 8)(x + 6)$$ on the interval $$-\frac{1}{5} < x < 2$$ given its zeros at $$x = -6$$, $

1. **Problem 4:** Simplify the expression $$\frac{3x^2 - x - 2}{2x - 2}$$. 2. **Step 1:** Factor numerator and denominator.

1. **State the problem:** Calculate the value of the expression $$(6 + 2) \times 5 - 4 \div 2$$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **Nyatakan masalah:** Cikgu Adam ingin mendaftar murid lelaki dan perempuan untuk kelas tuisyen dengan syarat:

1. **Problem:** Solve the quadratic equation $$4x^2 + 8x + 5 = 1$$ for $$x$$ using at least two methods and check the solutions. 2. **Step 1: Write the equation in standard form.**