Question

how would you factor (a+b)^2 - 64

Answer 1

64 is perfect square

Answer 2

\(x^2-y^2=(x+y)(x-y)\) you will need this difference of two perfect squares

Answer 3

\((a+b)^2\) this quantity is a perfect square by it self

Answer 4

any clue?
what is the number if we multiply it by it self we get 64

Answer 5

yeah the number would be 8

Answer 6

Good so you agree
that \(64=8*8=8^2\)

Answer 7

yes i do agree so I would break it apart by (a+8)(a-8) because its negative 64

Answer 8

no no! just follow
since you agreed now we can write
\((a+b)^2-64=(a+b)^2-8^2\)

Answer 9

yes?

Answer 10

ok yes i see that

Answer 11

now treat a+b as one entity let's call it z
a+b=z alright
so \((a+b)^2-8^2=z^2-8^2\)

Answer 12

i don't need to always call it some name i just want to explain it to you so i becomes easy to deal with okay

Answer 13

yep no problem

Answer 14

now we have \(z^2-8^2\) difference of two square
like is said before \(x^2-y^2=(x-y)(x+y)\)
we do the same with \(z^2-8^2=(z-8)(z+8)\)

Answer 15

yes?!

Answer 16

yes

Answer 17

now z=a+b
because i just called z it was a+b
so i have \(z^2-8^2=(z-8)(z+8)=(a+b-8)(a+b+8)\)

Answer 18

So \((a+b)^2-64=(a+b-8)(a+b+8)\)

Answer 19

ok that makes so much more sense thank you for your help

Answer 20

My pleasure!
once you know how to do it
you don't need all those steps
you go directly to write you factored form
because we know that's the difference of two perfect squares

Answer 21

yeah i understood the difference of perfect squares i was just confusing myself when i had to difference of perfect squares to combine

Answer 22

the only step you need is
\((a+b)^2-64=(a+b)^2-8^2\) then you write what it is directly

Answer 23

if you foil this \((x+y)(x-y)\) you will get \(x^2-y^2\) which is called difference of perfect squares

Answer 24

yeah i understand that now thank you do you think you can help with other problem too?

Answer 25

welcome! actually i have to go out now
sorry

Answer 26

ok no problem

Answer 27

oh if my help satisfied you there is best response thing click on it^_^