Question

use the distributive property to factor the expression. 10 + 35x ?(2 + x) this number should be

Explanation:

Step1: Find GCF of 10 and 35

The factors of 10 are \(1, 2, 5, 10\), and factors of 35 are \(1, 5, 7, 35\). The greatest common factor (GCF) is 5.

Step2: Apply distributive property

Using the distributive property \(ab + ac = a(b + c)\), we factor out 5 from \(10 + 35x\).
\(10\div5 = 2\) and \(35x\div5 = 7x\). So, \(10 + 35x = 5(2 + 7x)\).

Answer:

The first box (the green one) is 5, and the second box (the gray one) is 7. So the filled expression is \(5(2 + 7x)\), with the first missing number being 5 and the second being 7. If we are only asked for the number in the green box (the "?") as per the problem's "This number should be" hint, the answer is 5.