How do you Factor 16x^2 + 40xy + 25y^2?

Question

I am taking a correspondant class over the summer and cant seem to figure out how to work out this problem.

Answer 1

look at the first term :

16x^2

what two numbers can you multiply to get this number?

4x*4x

set it up like this

(4x )(4x )

no since they are all positive you put a plus sign in both of them

(4x+ )(4x+ )

no look at the last term:

25y^2

what two numbers can you multiply to get this?

5y*5y

so you put it like this

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

when you multiply the two outsides you get 20xy and when you multiply the two insides you get 20xy and when you add them you get 40xy(which is your middle term)

answer:

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

Answer 2

two numbers that multiply to 15x25 = 400 and add to 40

the two numbers are 20 and 20

16x^2 + 20xy + 20xy + 25y^2

factor by groups
(16x^2 + 20xy) + (20xy + 25y^2)

factor out GCF
4x (4x + 5y) + 5y (4x + 5y)

factor out (4x + 5y)

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

or (4x + 5y)^2

Answer 3

(4x+5y)^2

4x*4x=16x^2
5y*5y=25y^2
4x*5y=20xy doubled because you are squaring the terms so it is 40xy

16x^2+40xy+25y^2

Answer 4

16x^2 + 40 xy + 25y^2 =
(4x)^2 +2(4x)(5y) + (5y)^2 =
(4x + 5y)^2