Question

which expressions product is modeled by the tiles? (2x + 1)(x + 1)

Explanation:

Step1: Analyze the tiles

We have 1 \(x^{2}\) - tile, 4 \(x\) - tiles and 4 unit - tiles.

Step2: Expand the expressions

Expand \((2x + 1)(x+1)\) using FOIL method. \((2x + 1)(x + 1)=2x\times x+2x\times1+1\times x + 1\times1=2x^{2}+2x+x + 1=2x^{2}+3x + 1\), which is not correct.
Let's consider \((x + 2)(x + 2)\). Using FOIL: \((x + 2)(x + 2)=x\times x+x\times2+2\times x+2\times2=x^{2}+2x+2x + 4=x^{2}+4x + 4\), which matches the tiles (1 \(x^{2}\), 4 \(x\) and 4 units).

Answer:

\((x + 2)(x + 2)\)