# Creating and Manipulating Linear and Quadratic Expressions Stage 4 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Creating and Manipulating Linear and Quadratic Expressions - Stage 4.

### Relative Powers

##### KS 4 Short Challenge Level:

Weekly Problem 10 - 2007
The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?

### Divisible Expression

##### KS 4 Short Challenge Level:

Weekly Problem 39 - 2009
Can you show this algebraic expression is divisible by 4?

### Little Difference

##### KS 4 Short Challenge Level:

Weekly Problem 30 - 2014
What is the value of $2006 \times 2008 - 2007 \times 2007$?

### Brian's Number

##### KS 4 Short Challenge Level:

Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.

### Thousands of X

##### KS 4 Short Challenge Level:

Solve the equation $(x-2013)(x-2012)-(x-2012)(x-2011)=0.$

### Choir Boys

##### KS 4 Short Challenge Level:

Can you work out how many members this choir has from these percentages?