Question

1. which set of binomials were multiplied together to produce the product represented by these algebra tiles?$\boldsymbol{\triangleright}$ view image description$\bigcirc$ $(2x^{2}+x)(x+1)LXB0\bigcirc$ $2x+3$$\bigcirc$ $(2x+1)(x+1)$

Explanation:

Step1: Sum the area tiles

$x^2 + x^2 + x + x + 1 = 2x^2 + 3x + 1$

Step2: Factor the quadratic

Find two binomials whose product is $2x^2 + 3x + 1$. Test $(2x+1)(x+1)$:
$(2x+1)(x+1) = 2x(x+1) + 1(x+1) = 2x^2 + 2x + x + 1 = 2x^2 + 3x + 1$

Step3: Match with options

The factored form matches one of the given options.

Answer:

$\boldsymbol{(2x + 1)(x + 1)}$