Question

multiply the binomials using the area (box) method (just like notes)
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!
$(x + 1)(x + 5)$

Explanation:

Step1: Fill the box with products

The binomial is \((x + 1)(x + 5)\). The first row of the box has \(x\) and \(+1\), and the first column has \(x\) and \(+5\).

• Multiply \(x\) (row) and \(x\) (column): \(x\times x = x^{2}\)
• Multiply \(x\) (row) and \(+1\) (column): \(x\times1 = x\)
• Multiply \(+5\) (row) and \(x\) (column): \(5\times x = 5x\)
• Multiply \(+5\) (row) and \(+1\) (column): \(5\times1 = 5\)

Step2: Combine like terms

Now, we sum up all the terms from the box: \(x^{2}+x + 5x+5\).
Combine the like terms \(x\) and \(5x\): \(x + 5x=6x\).

Answer:

\(x^{2}+6x + 5\)