🧮 algebra

1. The problem asks us to determine whether each expression is odd or even, given that $k$ is an even number. 2. Recall the definitions:

1. **State the problem:** Simplify the expression $9x + 2y - 4x + 11 - 6y + 5$. 2. **Group like terms:** Combine the terms with $x$, the terms with $y$, and the constant terms sepa

1. **Problem (a): Compare $\frac{2}{3}$ of $\frac{3}{4}$ and $\frac{3}{4}$ of $\frac{2}{3}$.** 2. "Of" means multiplication, so calculate each:

1. **State the problem:** Simplify the expression $$\frac{5x^{3}(3x^{4}y^{2})^{3}}{27(x^{5}y^{2})^{2}x^{3}y}$$ given $x=2$ and $y=444$. 2. **Simplify the numerator:**

1. The problem involves finding the values of terms A, B, and C given the sums of terms involving f. 2. From the first graph example, we see that adding 9x, 5x, and 3x gives 14x, a

1. **State the problem:** Simplify the expression $5np + 7n + 5 + 3np + n + p$. 2. **Group like terms:** Group terms with $np$, terms with $n$, terms with $p$, and constants separa

1. Stating the problem: Solve the quadratic equation $u^2 + 9u + 14 = 0$. 2. Factor the quadratic: We look for two numbers that multiply to 14 and add to 9. These numbers are 7 and

1. **State the problem:** Simplify the expression $8a + 7d - 3a + 2v - 5d + 4v$. 2. **Group like terms:** Combine terms with the same variable.

1. **State the problem:** Factor the expression $x^3 - 27$. 2. Recognize that $x^3 - 27$ is a difference of cubes since $27 = 3^3$.

1. The problem is to simplify the expression $$-6m + 8m$$. 2. Both terms have the variable $m$, so we can combine them by adding their coefficients.

1. **State the problem:** Write the expression $$\frac{4 - \sqrt{3}}{\sqrt{3}}$$ in the form $$\frac{a\sqrt{3} + b}{c}$$ where $a$, $b$, and $c$ are integers. 2. **Start with the g

1. **State the problem:** Write $\frac{3\sqrt{3}}{4} - \frac{2}{\sqrt{3}}$ in the form $a\sqrt{3} + \frac{b}{c}$ where $a$, $b$, and $c$ are integers. 2. **Rewrite the expression:*

1. Problem: Factorise each expression. (a) $x^3 + 2x^2$

1. The first problem is to simplify the expression $\frac{3\sqrt{3}}{2} - 2$.\n\n2. The second problem is to write $4 - \sqrt{3} - \sqrt{5}$ in the form $a\sqrt{3} + b\sqrt{5} + c$

1. The problem asks to fill in the missing terms for sequences B and C based on the given terms and nth term formulas. 2. For Sequence A, the nth term is given as $21 - n$. The ter

1. **State the problem:** We want to write the expression $$\frac{2\sqrt{3}}{4 - \sqrt{5}} - 2$$ in the form $$a\sqrt{3} + b$$ where $a$, $b$, and $c$ are integers. 2. **Rationaliz

1. **State the problem:** Write $\frac{4 - \sqrt{3}}{\sqrt{3}}$ in the form $\frac{a\sqrt{3} + b}{c}$ where $a$, $b$, and $c$ are integers. 2. **Start with the given expression:**

1. **State the problem:** We know that one recycled glass bottle saves enough energy to power a computer for 25 minutes. 2. We want to find how many recycled glass bottles are need

1. The problem involves understanding the domain of the function $f(x) = \sqrt{4 - x}$. 2. The square root function requires the radicand (expression inside the root) to be non-neg

1. Stating the problem: Simplify the expression $$\frac{\frac{X^2}{16000}}{X}$$. 2. Rewrite the expression as a single fraction: $$\frac{X^2}{16000} \div X = \frac{X^2}{16000} \tim

1. **Work out the following, giving answers as mixed numbers in simplest form:** (1) $\frac{1}{2} + \frac{3}{4}$