Math Help - function help..

1. function help..

My homework is due within the hour online, and I can't seem to figure out this problem..

It says Evaluate F(3x+5)if f(x)=2x^2+2x+3

Now in the solutions manual it gives the follwing steps

f(3x+5)=2(3x+5)^2+2(3x+5)+3

= 2(9x^2+30x+25)+6x+10+3

=18x^2+66X+63

I get the whole problem except for- how did they get the 30x in the 2nd step? Can someone please tell me how they got the 30x? Thanks!

2. Originally Posted by Mathfailure
My homework is due within the hour online, and I can't seem to figure out this problem..

It says Evaluate F(3x+5)if f(x)=2x^2+2x+3

Now in the solutions manual it gives the follwing steps

f(3x+5)=2(3x+5)^2+2(3x+5)+3

= 2(9x^2+30x+25)+6x+10+3

=18x^2+66X+63

I get the whole problem except for- how did they get the 30x in the 2nd step? Can someone please tell me how they got the 30x? Thanks!
2(3x+5)^2 = 2*[9x^2 + 30x + 25]

Expand (3x + 5)^2, and you'll see it is 9x^2 + 30x + 25...

(3x + 5)*(3x + 5) = 9x + 15x + 15x + 25 (using FOIL).