Question

1. which set of binomials were multiplied together to produce the product represented by these algebra tiles?$square$ $(x + 5)LXB0square$ $(x + 3)(x + 2)$$square$ $(x + 2)(x + 2)$

Explanation:

Step1: Identify total area components

The area has: $4x^2$ (four blue squares), $5x$ (five green rectangles: four vertical + one horizontal), and $1$ (yellow square). So total area: $4x^2 +5x +1$

Step2: Factor the quadratic expression

Find two binomials whose product is $4x^2+5x+1$. We need factors of $4\times1=4$ that add to 5: 4 and 1.
Split the middle term: $4x^2 +4x +x +1$
Factor by grouping:
$4x(x+1) +1(x+1) = (4x+1)(x+1)$

Step3: Match to options

The factored form matches the option $(x+1)(4x+1)$ (or $(4x+1)(x+1)$, multiplication is commutative).

Answer:

$\boldsymbol{(4x + 1)(x + 1)}$ (corresponding to the third option shown)