Question

multiply the binomials using the area (box) method.
use the area model at the left (box method) to multiply out the following binomials.
after you multiply everything out in the box, then write your final answer below after you combine your like terms!
$(2x + 5)(3x - 4)$

Explanation:

Step1: Fill the box with products

First, multiply \(3x\) with \(2x\): \(3x\times2x = 6x^{2}\)
Then, multiply \(3x\) with \(+5\): \(3x\times5 = 15x\)
Next, multiply \(-4\) with \(2x\): \(-4\times2x = -8x\)
Finally, multiply \(-4\) with \(+5\): \(-4\times5 = -20\)

Step2: Combine like terms

Now, combine the middle terms (\(15x\) and \(-8x\)):
\(6x^{2}+15x - 8x - 20=6x^{2}+(15x - 8x)-20 = 6x^{2}+7x - 20\)

Answer:

\(6x^{2}+7x - 20\)