Gain a medal!
Bill 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.

Question

Gain a medal!
Bill 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.

anonymous · Answer

first off, lets factor,  x2 + 8x + 16, by grouping ourselves
x2+8x+16
x2+ 4x + 4x + 16
(x2+ 4x) + (4x + 16)
x(x+4) + 4(x + 4)
(x+4)(x+4)
(x+4)^2

now lets factor by a special product
x2+8x+16
a^2 + 2ab + b^2 = (a+b)^2
so,
a=1
b=4
do you see how I picked out 'a' and 'b'?