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If we attempt to create a square using the tiles that represent the algebraic expression on the left, A) how many \( x \)-tiles will you add to the length of the x-square tile B)How many unit tiles would you need to complete the square?

Ask by Barnett Donnelly. in the United States
Mar 13,2025

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A) Add 3 \(x\)-tiles to the length of the \(x\)-square tile. B) You need 9 unit tiles to complete the square.

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The Deep Dive

To form a perfect square using algebra tiles, you need to arrange your \( x \)-tiles (which represent the variable) in a square formation. The number of \( x \)-tiles you would add depends on the size of your \( x \)-square tile. If the side is \( x \), you would need to add \( x \) more \( x \)-tiles along the length to complete the square. For the unit tiles, if the expression is in a standard form like \( (x + a)^2 \), the unit tiles you'll need to fill the gap created by the \( a \) can be found by calculating \( a^2 \). This means you'll use \( a^2 \) unit tiles to complete the square, ensuring all space is perfectly filled with no gaps. It's like playing a matching game with tiles where every piece must fit snugly!

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