Question

Factor completely. 25w² + 60w + 36 Express the answer in the form (aw+b)2 . Enter your answer in the box.

Answer 1

Solution:

→25 w² + 60 w + 36

You can do it by two methods, either by splitting the middle term that is term containing w

Or, directly converting it into form of perfect square.

1. Splitting the middle term

=25 w² + 30 w + 30 w + 36

= 5 w× ( 5 w + 6) +6× ( 5 w + 6)

= ( 5 w + 6)(5 w + 6)

= (5 w + 6)²

2. By perfect square method

25 w² + 60 w + 36

= (5 w)² + 2 × (5 w)× (6) + (6)²

= (5 w + 6)²→→→using the Identity, (a+b)²= a²+ b²+ 2 a b

Answer 2

25w²=(5w)², 36=6², 60w=2*5w*6
Recall the formula (a+b)²=a²+2ab+b²
in this case, 25w² + 60w + 36=(5w+6)²