Question

Multiply and simplify: (x²+2x+2)(x²-2x+2) Please explain how you did it! Thank you!

Answer 1

again?

Answer 2

nobody helped me.

Answer 3

answer is
\[x^4+4\] and you have a choice. you can do 3 times 3 = 9 multiplications

Answer 4

oh sorry

Answer 5

you have to do 9 multiplications, but what is more interesting is to show
\[x^4+4=(x^2+2x+2)(x^2-2x+2)\]

Answer 6

wait why do you have to do nine? Not only three?

Answer 7

ok suppose you wanted to multiply two 3-digit numbers together. how many multiplications would you have to do? say

\[213\times 431\]

Answer 8

WEll i understand now!

Answer 9

really? great!

Answer 10

Yeah except i still need help! Just not on that part!

Answer 11

now in numbers we do it from the bottom up, starting at the ones place, then tens and so on. but with polynomials we usually to it from the top down because there is no borrowing or carrying

Answer 12

what do we do?

Answer 13

so if you just want
\[(x^2-2x+2)(x^2+2x+2)\] you have to do the following nine multiplications
\[x^2(x^2+2x+2)-2x(x^2+2x+2)+2(x^2+2x+2)\]
\[x^4+3x^3+2x^2-2x^3-4x^2-4x+2x^2+4x+4\]

Answer 14

see we have nine terms! nine, because of 3 terms times 3 terms means nine multiplications

Answer 15

Yeah I get it

Answer 16

now when you collect terms you get
\[x^4+4\] because in this case a bunch of stuff adds up to zero

Answer 17

Ok thanks so much!