Given the expression:
[tex]u^2+20u+100[/tex]To factor the given expression, we need two numbers the product of them = 100 and the sum of them = 20
We will factor the number 100
100 = 1 x 100 ⇒ 1 + 100 = 101
100 = 2 x 50 ⇒ 2 + 50 = 52
100 = 4 x 25 ⇒ 4 + 25 = 29
100 = 5 x 20 ⇒ 5 + 20 = 25
100 = 10 x 10 ⇒ 10 + 10 = 20
So, the suitable numbers are 10, 10
so, the factorization will be as follows:
[tex]u^2+20u+100=(u+10)(u+10)=(u+10)^2[/tex]The given expression is a complete square.
So, the answer will be (u+10)(u+10)
Or can be written as (u+10)²
