Area Model: Multiplying Brackets

Lesson 7 of 12 · 7 min · Free, no account needed

What you will learn

To expand brackets, build the rectangle: (x + a)(x + b) is one x², a + b strips and a × b unit squares.
Terms of the same kind are like terms: the strips add up, 3x + 3x = 6x.
(x + 3)² is not x² + 9: the two strips make it x² + 6x + 9.

(x + 3)² = x² + 9? Most people think so.
Take x = 5. How many unit squares fill a square with side x + 3? Drag the marker to your bet.
Build the square from x² and 9.
Drag each tile onto a hole that fits, or tap a tile. The tray holds exactly what the rule says.
How much did the rule forget?
Turn x and count. Find the x where the forgotten strips hold 30 unit squares.
Multiplying brackets is building a rectangle.
To expand (x + 3)(x + 3), fill the rectangle: every part of one side times every part of the other.
The two 3 by x strips are like terms: same shape, so they add. 3x + 3x = 6x.
So (x + 3)² = x² + 6x + 9. In general (x + a)(x + b) = x² + (a + b)x + ab.
Read off (x + 4)(x + 2).
Drag each tile into its bin, or tap a tile and then a bin.
Game: the tile shop.
Order exactly the tiles each frame needs, then Buy. Every tile too many or too few costs a coin.
Make your own frame.
Drag the blue handles to choose a and b in (x + a)(x + b). The tiles fill themselves.
Work out 103² in your head with the area model.
103 = 100 + 3. Add up the four tiles.
Your frame: the rule against the tiles.
Turn x and compare both formulas with the real count. Then pick the one that always matches.

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