Question

Factor completely 16x2 + 40x + 25.

(4x − 5)(4x − 5)

(2x − 5)(2x − 5)

(2x + 5)(2x + 5)

(4x + 5)(4x + 5)

Answer 1

Hello,

16x²+40x+25=(4x+5)²
Answer 4

Answer 2

The factors are :
`(4x+5)(4x+5)`

Explanation:

The given expression is :

`16x^(2) +40x+25`

Re writing the equation :

`4^(2)x^(2) +40x+5^(2)`

Applying the rule
`a^(x) b^(x) =(ab)^(x)`

`(4x)^(2) +40x+5^(2)`

Re write 40x as 2.4x.5

`(4x)^(2) + 2*4x*5+5^(2)`

Applying perfect square formula:

`(a+b)^(2)=a^(2) +2ab+b^(2)`

where a = 4x and b = 5

So, the factors become :
`(4x+5)^(2)`

or
`(4x+5)(4x+5)`