Question

can someone show me how to find the product (x^2+9)(x^3+6x+3)

Answer 1

multiply all of \(x^3+6x+3\) by \(x^2\) and then multiply it all by 9
then combine like terms

Answer 2

x^5+9*9? I am lost

Answer 3

ok lets go slow

Answer 4

ok

Answer 5

wow that came out garbled

Answer 6

\(x^2+9\) has two terms, \(x^3+6x+3\) has three terms so you are going to have to do \(2\times 3=6\) multiplications

Answer 7

it doesn't matter what order you do them in, but it is easiest to keep track of you multiply first everything in the \(x^3+6x+3\) by \(x^2\) and then multiply all of \(x^3+6x+3\) by 9

Answer 8

so we start with
\[(x^2+9)(x^3+6x+3)=x^2\times x^3+x^2\times 6x+x^2\times 3+9\times x^3+9\times 6x+9\times 3\]

Answer 9

i am following what you are saying so far

Answer 10

you usually skip that step, the one i wrote above, and go right to
\[x^5+6x^3+3x^2+9x^3+54x+27\]

Answer 11

then the only like terms to combine are \(6x^3+9x^3=15x^3\) so your "final answer" is
\[x^5+15x^3+3x^2+54x+27\]

Answer 12

I think one of the problems i have is ( ) * ( ) = multiplications but when you are + earlier got confusing when betweent he brackets the first bracket had x^2 second bracket had the + sign how do you know when to add vs using the multiplication sign?
does that make sense?

Answer 13

think of it this way
suppose you wanted to multiply \(12\times 213\)
you would have to do 6 multiplications, and then at the end some additions. this is like multiplying \((x+2)(2x^2+x+3)\) where \(x\) is ten

Answer 14

first you would write
213
12

and then you would multiply everything first by 2, then by 1 and then add them up

Answer 15

got that part

Answer 16

thanks