Question

(2a^x+.5b^x)^2

Answer 1

FOIL still applies...
\[\Large (2a^x + 0.5b^x)^2\]

Answer 2

Just remember that
\[\Large (a^x)^2 = a^{2x}\]\[\Large(b^x)^2=b^{2x}\]

Answer 3

the problem is i never really understood the whole foil thing

Answer 4

LOL That is a problem :)
Want me to run it through you again? ^_^

Answer 5

please and thank you :) i would appreciate it

Answer 6

Okay, say we have a to multiply a pair of binomials...
\[\Large (a + b)(x+y)\]

Answer 7

We basically FOIL it...

FOIL is an acronym...

First is...
product of the FIRST terms...
\[\Large (\color{red}a+b)(\color{red}x+y)=\color{blue}{ax}...\]

(... meaning we're not done yet)

Answer 8

When you go through the steps, you get\[(2a^x+.5b^x)^2=(2a^x+.5b^x)(2a^x+.5b^x)=4a^{2x}+2a^xb^x+.25b^{2x}\]

Answer 9

Next is...
product of the OUTER terms...
\[\Large (\color{red}a + b)(x+\color{red}y)=ax\color{blue}{+ay}...\]


Then...
product of the INNER terms...
\[\Large (a + \color{red}b)(\color{red}x+y)= ax + ay \color{blue}{+bx}...\]

Finally,
product of the LAST terms...
\[\Large (a + \color{red}b)(x+\color{red}y)= ax + ay + bx \color{blue}{+by}\]

Answer 10

And there you have it, FOIL.

Answer 11

Any questions?

Answer 12

uh.. let me go over that again my brother is being distracting.

Answer 13

You do that... and once you've gotten the hang of FOIL, keep in mind that
\[\Large (2a^x + 0.5b^x)^2=\color{blue}{(2a^x + 0.5b^x)(2a^x + 0.5b^x)}\]
So that FOIL may readily be applied...

Answer 14

oh okay i got it now!! thanks so much!

Answer 15

Great :)
Try doing FOIL, and you should end up with what AnimalAin got, if you did it properly :)

Answer 16

i did thanks guys so much