🧮 algebra

1. **State the problem:** Simplify the expression $$(a^3 - 2a^2) - (3a^2 - 4a^3)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign ov

1. **State the problem:** Simplify the expression $(5p^2 - 3) + (2p^2 - 3p^3)$. 2. **Write down the expression:**

1. **State the problem:** Graph the equation $x = -4$ by making a table of values. 2. **Understand the equation:** The equation $x = -4$ means that for every value of $y$, $x$ is a

1. **Stating the problem:** An investor receives 31000 in interest per annum from a sum of money invested partly at 10% and partly at 7% simple interest. If the amounts invested at

1. **State the problem:** Simplify the expression $5p - 3p + p$. 2. **Recall the rule:** When simplifying algebraic expressions, combine like terms by adding or subtracting their c

1. **State the problem:** Simplify the expression $$\frac{16 a^8 b^4}{8 a^3 b^2}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $0.88 = \frac{558 + x}{700 + x}$ for $x$. 2. **Use the formula:** To solve for $x$, multiply both sides by the denominator to eliminate

1. **State the problem:** We are given the function $f(x) = 3x^2 - 2x + \frac{1}{2}$ and want to understand its properties. 2. **Formula and rules:** This is a quadratic function o

1. **State the problem:** We need to find the equation of a line parallel to line A that passes through point P(0, 3). 2. **Find the slope of line A:** The slope $m$ is given by th

1. **Nyatakan masalah:** Cari punca-punca bagi persamaan kuadratik $$x^2 + 8 = 6 + 3x$$. 2. **Susun semula persamaan supaya berbentuk $$ax^2 + bx + c = 0$$:**

1. The problem is to find the greatest value of $t$ where two given functions are equal. 2. To solve this, we set the two functions equal to each other: $$f(t) = g(t)$$

1. **State the problem:** We are given two functions: $$f(x) = \frac{x + 3}{\sqrt{x^2 - 1}}$$

1. **State the problem:** Simplify the expression $$\frac{5p^{4} \times (3q^{3})^{2}}{15p^{6}q^{4}}$$. 2. **Apply the exponent rule:** Recall that $ (a^m)^n = a^{m \times n} $. So,

1. **State the problem:** We need to analyze and draw the graph of the function $$f(x) = 3 - \sqrt{2 - x}$$. 2. **Understand the domain:** The expression under the square root must

1. **Nyatakan masalah:** Kita perlu menyederhanakan ekspresi $$\frac{(2x^5 y^{-3})^4}{(x^2 y)^5}$$. 2. **Gunakan hukum pangkat:** Untuk pangkat pada perkalian, gunakan $$ (ab)^n =

1. **State the problem:** Find the domain and range of the function $$f(x) = \frac{3}{\sqrt{9 - x^2}}$$. 2. **Understand the domain constraints:** The expression under the square r

1. **State the problem:** We need to find the possible values of $k$ such that the constant term in the expansion of $\left(x^2 + x^k\right)^{12}$ has a coefficient of 495. 2. **Re

1. The problem asks to identify the pattern of the decay sequence and then find the total decay in the first 5 seconds. 2. The given decay numbers are 24300, 8100, 2700, ...

1. **State the problem:** Solve the equation $x^2 + 9x + 7 = -x^2 - 2$ for $x$. 2. **Bring all terms to one side:** Add $x^2$ and $2$ to both sides to combine like terms:

1. The problem is to solve the equation shown in question 3 (assuming it is a typical algebraic equation). Since the exact equation is not provided, let's consider a common example

1. **State the problem:** Solve the system by substitution: $$y = 6x - 11$$