Explore this interactive math tool and try to figure out what's happening on your own. How does this demonstration help you discover the value of (*a* + *b*)^{2}?

If you need some help, follow the steps below and click on the buttons only when instructed.

- Arrange the colored shapes so that they completely cover the large white square. When finished, click the
**Fit Shapes to Square** button. This will align the shapes within the square, and it may even show you an arrangement of the pieces that differs from yours. - Compare the length of the large white square to the lengths of the smaller shapes. (You can do this by dragging the shapes to the slider at top.)
- How do the dimensions of the shapes and the large white square compare to the lengths of
*a* and *b*? - Click the
**Show Dimensions of Square** button. - What do you notice about the length of one side of the large white square, in comparison to the lengths of the smaller shapes?
- Move the shapes around to see if this is always true.
- Click the
**Reset** button. Now click the **Show Square Dimensions** button. Does the information shown confirm your answers to the questions above?

- What happens if the dimensions change?
- Drag the red dot in the middle of the slider to change the size of
*a* and *b*. - Fit the newly sized shapes in the large square by clicking the
**Fit Shapes to Square** button. - Do your answers still hold?

- Determine the area of each of the colored shapes.
- Click the
**Reset** button. Then click the **Show Dimensions of Square** button. Press the **Fit Shapes to Square** button to align the shapes. - What is the area of the large white square?
- What is the area of the yellow square?
- What is the area of the blue square?
- What is the area of the red and green rectangles? Are they equal?

- Compare the areas.
- What is the sum of the area of the colored shapes?
- Figure out the answer, and then click the
**Show All Areas** button. - How does the area of the large white square compare to the sum of the areas of the colored shapes?

- State your final conclusion.