Lesson Goals
- Review the distributive property in the context of quadratic relations.
- Expand an expression by multiplying or squaring binomials.
- Expand and simplify equations of quadratic relations so that they are in standard form.
- Extend the distributive property beyond multiplying two binomials.
Try This
A square has side lengths of \(w\) units. The square's side lengths are then increased by \(3\) units on each side.
Square 1
Square 2
Let \(\Delta A\) represent the difference in the areas of the two squares (Square 2 minus Square 1).
For example when \(w=2\), the area of Square 1 is \(2^2=4\).
The side lengths of Square 2 are \(5\) units, and the area of this square is \(5^2=25\).
So, for \(w=2\), then \(\Delta A = 25-4\) , or \(\Delta A = 21\).
Determine a simplified equation expressing \(\Delta A\) in terms of \(w\).
That is, find an equation that allows you to calculate the difference in areas directly from the original side length without having to find the two areas first.