# Expanding and Factorising Quadratics - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Expanding and Factorising Quadratics.

### Square and Cube

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 24 - 2014
The square of a positive number is twice as big as the cube of that number. What is the number?

### Two Girls

##### KS 4 Short Challenge Level:

Weekly Problem 45 - 2012
There are 10 girls in a mixed class. If two pupils are selected, the probability that they are both girls is 0.15. How many boys are in the class?

### Divisible Expression

##### KS 4 Short Challenge Level:

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

### Square Product

##### KS 4 Short Challenge Level:

Weekly Problem 10 - 2011
Will this product give a perfect square?

### Little Difference

##### KS 4 Short Challenge Level:

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