Simplify (8x^2 + 36x)/(2x + 9) and explain why it is an even expression.

You have to understand what makes an expression even. Even numbers are formed by either two odd numbers being added together or an even number x an odd number. We can start by looking at the denominator. Immediately we can see that 2x+9 cant be simplified into anything this is because there isnt a number that is a factor or 2 and 9. We can also see that the denominator has an x expression where as the top has x^2. Now down to the simplifying. We can see from the numerator that we can take out a factor of 4x as this goes into 8x^2 and 36x. Giving us 4x(2x+9). straightaway we can see that the number and denominator are the same. We can no cancel them out. leaving us with (8x^2 + 36x)/(2x + 9) = 4x4 is an even number and since any number multiplied by an even number is even. We have proven that the expression (8x^2 + 36x)/(2x + 9) is even