Question

how do I square a binomial (2a-2b)^2??? Can someone show me formula?

Answer 1

hello rosanne!

Answer 2

hi satellite!!! how r u? I have a final on mon for this class. Im going to have to bust my retricegetting this down perfect.

Answer 3

bust my buttt*

Answer 4

yeah make sure to bust your retrice. whatever that is! lol

Answer 5

yes sure! all u have to do is the follow the rule...

perfect squares:(x-b)^2= x^2 -2xb+b^2

Answer 6

just make sure when you see
\[(\text{this + that})^2\] to write
\[(\text{this + that})\times (\text{this + that})\] and you will get it right

Answer 7

\[(2a-2b)^2=(2a-2b)(2a-2b)=4a^2-4ab-4ab+4b^2\]
\[=4a^2-8ab+4b^2\]

Answer 8

why did u subtract?

Answer 9

be careful with the plus and minus signs, and make sure to do FOUR multiplications and not say something silly like
\[(a+b)^2=a^2+b^2\] which is absolutely wrong. math teacher hate that

Answer 10

lets go slow

Answer 11

\[(2a-2b)^2=(2a-2b)(2a-2b)\] so far so good?

Answer 12

why r u subtracting?

Answer 13

i just copied down exactly what you wrote. i have done nothing else. you wrote
\[(2a-2b)^2\] yes?

Answer 14

never mind

Answer 15

sorry

Answer 16

ok we continue

Answer 17

you have to do 4 multiplications.

Answer 18

ok

Answer 19

first step is?

Answer 20

\[2a\times 2a\]
\[2a\times (-2b)\]
\[(-2b)\times 2a\]
\[(-2b)\times (-2b)\]

sometimes this is called foil for "first outer inner last"

Answer 21

that is after you write
\[(2a-2b)^2=(2a-2b)(2a-2b)\] then you do 4 multiplications as i wrote above

Answer 22

now we compute as follows
\[(2a)\times (2a)=4a^2\]
\[2a\times (-2b)=-4ab\]
\[(-2b)\times (2a)=-4ab\]
\[(-2b)\times (-2b)=+4b^2\]
are these clear?

Answer 23

wait u lost me why did u put a -2
'

Answer 24

because i am thinking as follows
\[(2a-2b)=2a+(-2b)\] the minus sign comes with the variable. you cannot ignore it

Answer 25

so i would say the first term in
\[2a-2b\] is
\[2a\] and the second term is
\[-2b\] you have to keep the minus sign

Answer 26

oh ok i c

Answer 27

ok good. so now we have the following after doing FOUR multiplications: \[4a^2-4ab-4ab+4b^2\] remember the signs count. they are important

Answer 28

make sure you know that the signs are correct. now the last step is to comine
\[-4ab-4ab\] and that is
\[-8ab\]

Answer 29

because you think "minus 4 minus 4 is minus 8"

Answer 30

so your "final answer" is
\[4a^2-8ab+4b^2\]

Answer 31

we can do another one if you like

Answer 32

I still like just standard distribution:
\[(2a - 2b)^2 \]\[= (2a - 2b)(2a-2b)\]\[=2a(2a-2b) - 2b(2a-2b)\]\[=4a^2 - 4ab - 4ab +4b^2\]\[=4a^2 - 8ab + 4b^2\]

Answer 33

It always works with any number of factors and terms.