Question

Could someone help me with this one...?
Billy wants to factor x2 + 8x + 16 by grouping; however, Sara says it is a special product and can factor a different way. Using complete sentences, explain and demonstrate how both methods will result in the same factors.

Answer 1

whats your attempt ?

Answer 2

one way (of grouping) is that you first find 2 numbers whose sum is 8 and product is 16

Answer 3

can u find these 2 numbers?

Answer 4

yes1 so split 8x as 4x and 4x
now here comes the grouping part
(x^2+4x) +(4x+16)

Answer 5

you still haven't factored right ?
factor out 'x' from 1st group and 4 from 2nd group , what u get?

Answer 6

what seems to be common from x^2+4x ?
x^2=x*x and 4x=4*x

Answer 7

i just see x common in both.
so, x^2+4x = x (x+4)
agree ?

Answer 8

4x +16 = ...?

Answer 9

yeah

Answer 10

x is the gcf of 1st group only...

Answer 11

whats common in 4x +16 ??

Answer 12

the 1st group (x^2+4x) = x(x+4)
2nd group (4x+16) = 4(x+4)
now whats common in both groups ?

Answer 13

i don't see 'awesome' in any of the groups, how can it be common :P

Answer 14

yes, 4 is gcf of 2nd group.

Answer 15

the 1st group (x^2+4x) = x\( \huge (x+4)\)
2nd group (4x+16) = 4\( \huge (x+4) \)

once again, whats common in both groups ?

Answer 16

we r not yet done with factor by grouping...

Answer 17

you note that x+4 is common from both group, so we can factor it out