Creating and manipulating expressions and formulae

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Find all the solutions to the this equation.

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.

Can you find the area of a parallelogram defined by two vectors?

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.