Question

what is the simpler form of each product: (8m+1)^2
the answer id 64m^2+16m+1, now I get where the 64m^2 and the 1 came from, Im confused about how 16m came to be part of the equation, can someone please explain?

Answer 1

(a+b)^2 = (a+b)*(a+b)
Applying distributive rule
(a+b)^2 = (a+b)*a + (a+b)*b
(a+b)^2 = a*a+b*a + a*b+b*b
Note that a*a=a^2 and a*b=b*a
(a+b)^2 = a^2+ 2*(a*b) + b^2
So:
(8m+1)^2 = (8m)^2+ 2*((8m)*1) + (1)^2
(8m+1)^2 = (8^2)*(m^2)+ 2*8*m*1 + 1
(8m+1)^2 = (64)*(m^2)+ 16*m + 1
(8m+1)^2 = 64m^2+ 16m + 1
Hope that helps!

Answer 2

Yes that helps, Thanks :)