🧮 algebra

1. Find the highest common factor (HCF) of $12x^{12}$ and $16x^{16}$. The HCF of two terms is found by taking the HCF of the coefficients and the lowest power of common variables.

1. **Problem 474:** Simplify $$2(m - n)^2 (m + n) - 2(m + n)^2 (n - m) - 4m(m - n)(m + n)$$ 2. **Step 1:** Expand and rewrite terms.

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

1. The problem states that we have a square with side length $s$ and asks for two algebraic expressions using different operations to represent the perimeter of the square. 2. The

1. The problem asks to determine how many terms the expression $xyz$ has and whether Greg's reasoning about the number of terms is correct. 2. Recall that in algebra, a term is a p

1. **State the problem:** We need to find the average amount of money spent per customer in May, given that the number of customers increased by 16% from April and the total money

1. The problem states: 26% of $c$ is equal to 65% of $d$. We want to find what percent of $c$ equals $d$, i.e., find the number $x$ such that $d = x\%$ of $c$. 2. Write the equatio

1. **State the problem:** We are given the function $$y = 0.9x + \frac{x^2}{15}$$ and asked to draw its graph for $$0 \leq x \leq 35$$ where $$x$$ represents speed (in m/s) and $$y

1. **Stel het probleem vast:** Vereenvoudig de uitdrukking zonder negatieve of gebroken exponenten. 2. **Gebruik de exponentregels:**

1. **Probleemstelling:** Schrijf zonder negatieve en/of gebroken exponenten de volgende uitdrukkingen. 2. **Formules en regels:**

1. **Stel het probleem vast:** Schrijf de uitdrukking $x^{-1}$ zonder negatieve of gebroken exponenten. 2. **Formule en regels:** Een negatieve exponent betekent dat je de basis on

1. Stating the problem: Simplify the expression $$\frac{25t}{7u} \times \frac{14}{15t}$$. 2. Write the expression as a single fraction: $$\frac{25t}{7u} \times \frac{14}{15t} = \fr

1. **State the problem:** Solve the quadratic equation $$x^2 + 5x + 12 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions a

1. **State the problem:** Solve the system of linear equations: $$2x + 2y = 8$$

1. **State the problem:** Solve the system of equations using the elimination method. Given system:

1. **State the problem:** We are given a line $L$ with equation $3y - 4x = 21$ and a point $P(15, 2)$. We need to find the equation of the line perpendicular to $L$ that passes thr

1. **State the problem:** We are given a line $L$ with equation $2x + 3y = 7$ and need to find which of the given lines is perpendicular to $L$. 2. **Recall the rule for perpendicu

1. Problem 21: Given the equation $y = 3x - 2$, find $y$ when $x = 10$. 2. Substitute $x = 10$ into the equation:

1. Calculate $2 \left( \frac{3}{5} \right)^2$. First, square $\frac{3}{5}$:

1. Express $\frac{12}{5}$ as a mixed fraction. - Divide 12 by 5: $12 \div 5 = 2$ remainder $2$.

1. The problem is to simplify the expression \(\frac{0,(7) + 1}{0,(7) + 2} - \frac{7}{176} \div \frac{0,(81) + 1}{0,(81) + 2}\). 2. First, convert the repeating decimals to fractio