Respuesta :
Answer:
[tex]x^6+x^4+4x^3-2x^2-x+3[/tex]
Step-by-step explanation:
[tex]x^3+2x+3[/tex]
[tex]\times(x^3-x+1)[/tex]
---------------------------------
First step multiply your terms in your first expression just to the 1 in the second expression like so:
[tex]x^3+2x+3[/tex]
[tex]\times(x^3-x+1)[/tex]
---------------------------------
[tex]x^3+2x+3[/tex] Anything times 1 is that anything.
That is, [tex](x^3+2x+3) \cdot 1=x^3+2x+3[/tex].
Now we are going to take the top expression and multiply it to the -x in the second expression. [tex]-x(x^3+2x+3)=-x^4-2x^2-3x[/tex]. We are going to put this product right under our previous product.
[tex]x^3+2x+3[/tex]
[tex]\times(x^3-x+1)[/tex]
---------------------------------
[tex]x^3+2x+3[/tex]
[tex]-x^4-2x^2-3x[/tex]
We still have one more multiplication but before we do that I'm going to put some 0 place holders in and get my like terms lined up for the later addition:
[tex]x^3+2x+3[/tex]
[tex]\times(x^3-x+1)[/tex]
---------------------------------
[tex]0x^4+x^3+0x^2+2x+3[/tex]
[tex]-x^4+0x^3-2x^2-3x+0[/tex]
Now for the last multiplication, we are going to take the top expression and multiply it to x^3 giving us [tex]x^3(x^3+2x+3)=x^6+2x^4+3x^3[/tex]. (I'm going to put this product underneath our other 2 products):
[tex]x^3+2x+3[/tex]
[tex]\times(x^3-x+1)[/tex]
---------------------------------
[tex]0x^4+x^3+0x^2+2x+3[/tex]
[tex]-x^4+0x^3-2x^2-3x+0[/tex]
[tex]x^6+2x^4+3x^3[/tex]
I'm going to again insert some zero placeholders to help me line up my like terms for the addition.
[tex]x^3+2x+3[/tex]
[tex]\times(x^3-x+1)[/tex]
---------------------------------
[tex]0x^6+0x^4+x^3+0x^2+2x+3[/tex]
[tex]0x^6-x^4+0x^3-2x^2-3x+0[/tex]
[tex]x^6+2x^4+3x^3+0x^2+0x+0[/tex]
----------------------------------------------------Adding the three products!
[tex]x^6+x^4+4x^3-2x^2-x+3[/tex]
