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🟦 Algebra Tiles

Drag and rotate tiles to build expressions and discover how completing the square works — visually and hands-on.

Algebra Tiles
Drag to move  ·  Double-click or double-tap to rotate 90°
Add tiles
x² tile
x tile
1 tile
−x tile
−1 tile
Expression
0
Legend
x² (x by x)
x tile (x by 1)
1 tile (1 by 1)
−x tile
−1 tile
Add tiles and arrange them. Try: 1 x² tile + 6 x tiles, then complete the square with 1-tiles!

How to complete the square with tiles

1
Start your expression
Add 1 blue x² tile and an even number of green x tiles (try 6).
2
Arrange into an L
Place the x² in the top-left corner. Split your x-tiles evenly — half along the right edge, half along the bottom.
3
Find the missing corner
There's a gap in the bottom-right. How many 1-tiles fill it perfectly? That number is (b/2)².
4
Complete the square!
Fill in the corner and the hint box confirms your perfect square — and shows you the factored form.