Use a special product formula to factor the perfect square trinomial.?

Question

b2 + 8b + 16

Answer 1

b^2 + 8b + 16
= b^2 + 2*b*4 + 4^2
= (b+4)^2

Answer 2

Here's how to recognise a perfect square trinomial: There's something squared on each end, and twice the product of the two roots in the middle. Here, you have b^2 and 4^2 on each end, and 2*b*4 = 8b in the middle. So write a pair of parenthesis
( )
and put in between them the sign between the first two terms, whether - or +. Here, it's +. Note, the sign between the second two terms will always be + for real number coeffieiccnts.) So now you have
( + )
Finally, put the two roots in the spaces and an exponent ^2 on the outside.:
(b + 4)^2
To prove it, put the factors side by side and multply them out.
(b + 4 )(b + 4) = b^2 + 4b + 4b + 16 = b^2 + 8b + 16
Try this yourself a few times with different examples and you'll get the hang of it. Good luck on your test!

Answer 3

b2 + 8b + 16=(b + 4)^2

Answer 4

(b+a)² = b² + 2ab + a². The middle term is 8b = 2ab ---> a=4.

The third term a² = 16 is OK for a=4.

So (b+4)² is the answer.

Answer 5

(a+b)(a+b)= a^2 +2ab +b^2 = (a+b)^2
So b^2 +8b+16 = (b+4)(b+4) = (b+4)^2

Answer 6

b | 4 | 4b
b | 4 | 4b
----------------
b^2 | 16 | 8b

Therefore,
b^2 + 8b + 16 = (b + 4)(b + 4) = (b + 4)^2

Answer 7

Looking at it, you see that 9 =3^2 and 64 = -8^2 so it factors to (3x-8)^2

Answer 8

(b-4)^2