An algebra tiles activity forms a rectangle; which equation represents the area and its factorization?

An algebra tiles activity forms a rectangle; which equation represents the area and its factorization?

• A. 2(x+2) = 2x + 4
• B. x(2x+4) = 2x^2+4x
• C. (x+2)^2 = x^2+4x+4
• D. 2x+4 = x^2+2x

Answer: (A)

In algebra tiles, the area of a rectangle is found by multiplying its length and its width. The tiles in this rectangle form a width of 2 and a length of (x+2), so the area is 2 times (x+2). Writing that as a product shows the factorization: 2(x+2). If you expand it, you get 2x + 4, which matches the same area written in standard form. This is exactly what the equation demonstrates: the area factored as 2(x+2) equals its expanded form 2x+4. The other expressions don’t fit the tile arrangement: x(2x+4) would imply a rectangle with dimensions x and (2x+4), giving area 2x^2 + 4x, which isn’t what the tiles show. (x+2)^2 corresponds to a square with side x+2, yielding x^2 + 4x + 4, not the 2-by-(x+2) rectangle. And 2x+4 = x^2 + 2x would mix terms that don’t align with the same rectangle's area.

In algebra tiles, the area of a rectangle is found by multiplying its length and its width. The tiles in this rectangle form a width of 2 and a length of (x+2), so the area is 2 times (x+2). Writing that as a product shows the factorization: 2(x+2). If you expand it, you get 2x + 4, which matches the same area written in standard form. This is exactly what the equation demonstrates: the area factored as 2(x+2) equals its expanded form 2x+4.

The other expressions don’t fit the tile arrangement: x(2x+4) would imply a rectangle with dimensions x and (2x+4), giving area 2x^2 + 4x, which isn’t what the tiles show. (x+2)^2 corresponds to a square with side x+2, yielding x^2 + 4x + 4, not the 2-by-(x+2) rectangle. And 2x+4 = x^2 + 2x would mix terms that don’t align with the same rectangle's area.