Question

which area model represents the factorization $6x^{2}+10x + 4=(3x + 2)(2x + 2)$?

Explanation:

Step1: Expand the factored form

Use FOIL method on $(3x+2)(2x+2)$:
$$(3x)(2x) + (3x)(2) + (2)(2x) + (2)(2)$$

Step2: Calculate each term

Compute individual products:
$$6x^2 + 6x + 4x + 4$$

Step3: Combine like terms

Add the linear terms:
$$6x^2 + 10x + 4$$

Step4: Verify area components

The expanded polynomial needs: 6 $x^2$ tiles, 10 $x$ tiles, 4 unit tiles. The bottom model has 6 $x^2$ tiles, 4 + 6 = 10 $x$ tiles, and 4 unit tiles (implied by the structure matching the factorization), while the top model only has 2 $x^2$ tiles, which is incorrect.

Answer:

The bottom area model (with 6 $x^2$ tiles, 10 $x$ tiles, and 4 unit tiles) represents the given factorization.