Question

PLEASE HELP URGENT!!
Chase wants to factor x^2 + 10x + 25 by grouping; however, Paige 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

factor by grouping:
x^2 + 10x + 25
= x^2+ 5x + 5x + 25
= x(x + 5) + 5 (x + 5)
= (x + 5)( x + 5)

Answer 2

thank you so much for that :)

Answer 3

what does a special product mean and what is another method I can use ? @welshfella

Answer 4

well I guess because 25 is a perfect square and we have 2*5 = 10 for the coefficient of x, we can use the following special product identity:

(x + a)^2 = x^2 + 2ax + a^2

here a^2 = 25 so a = 5 and 2a = 2*5 = 10

Answer 5

another example of en expression where we could apply the same identity would b x^2 + 6x + 9

Answer 6

9 =3^2 and 2*3 = 6

Answer 7

Oh ok I understand now, thanks a bunch! :)

Answer 8

yw