ShmoopTube

00:00

Sorry and here's your smoked you sure Brought to you

00:04

by dogs full of homework You might be excited when

00:07

you pass but just imagine how your dog feels All

00:12

right Which of the following is equivalent to twenty five

00:14

x to the fourth power minus sixty x squared y

00:17

squared plus thirty six y to the fourth power And

00:20

here the potential answers are equivalent to so yeah we're

00:23

gonna factor a whole bunch of parentheses Alright big coefficients

00:27

A couple of different variables Gobs of exponents I guess

00:31

we should start feeding our dog our homework Right This

00:34

one is way simpler than it looks We need toe

00:37

not get fido involved The trick here is to recognize

00:40

that the expression where given is really the difference of

00:42

two squares squared So check out the first and last

00:46

term's twenty five x of the fourth and thirty six

00:49

Why To the fourth notice anything interesting about those values

00:52

Yeah they're both perfect squares Square room twenty five five

00:55

hundred thirty six is six and x squared times X

00:58

squared will get us x to the forth So that

01:01

part works out as well The other big thing to

01:03

notice is that there's a negative in there Which means

01:06

that whatever this factors into must include at least one

01:10

minus side only options being d or way too positive

01:14

there's No way you could ever get to that negative

01:16

sixty x squared y squared in the middle because no

01:20

matter how you slice it everything will always multiply out

01:23

to be positive right away We can eliminate those doing

01:26

knuckleheads Which leaves us just a and c is possible

01:29

answers Well at this point we can multiply through for

01:31

each of them until we find a result that matches

01:34

the expression we've been given We should start by re

01:37

writing it this way Five x squared minus six y

01:39

squared times five x squared minus six y squared Then

01:44

we just distribute our way through this thing Well we

01:47

get twenty five x of the fourth minus thirty x

01:49

squared y squared minus another thirty x squared y squared

01:53

plus thirty six Why To the fourth Well after adding

01:56

like terms were left with twenty five x to the

01:58

fourth minus c like the x squared y squared plus

02:01

thirty six y to the fourth and boom We've got

02:05

our answer It's option a c totally not worth freaking

02:08

out about in framing your best friend now Besides he

02:11

still full from your sister's rhetoric essay from last night

Full Transcript