Question

Use the FOIL method to simplify the binomials.
(y-3) (2y^3-4y+5)
show all work

Answer 1

there is no such thing as the foil method, that is a lie made up by math teachers

Answer 2

did the question really say "simplify" and really say "foil"?

Answer 3

@satellite73 I'm pretty sure the "foil" method is real

Answer 4

i am pretty sure it is not

Answer 5

yes this is what the problem said

Answer 6

okay thanks for your help

Answer 7

"foil" is a mnemonic device to remember to do 4 multipications when you have two terms by two terms
"first, outer, inner, last'"\[(a+b)(c+d)=ac+ad+bc+bc\]

Answer 8

but here you have not two terms by two terms but two terms by 3 terms, meaning you have to do not four but SIX multiplications, more letters than in "foil"

Answer 9

\[(y-3) (2y^3-4y+5) \]
\[=y\times 2y^3+y\times (-4y)+y\times 5-3\times 2y^3-3\times (-4y) -3\times 5\]

Answer 10

you don't really write that of course, just go to
\[2y^4-4y^2+5y-6y^3+12y-15\]

Answer 11

then combine like terms

Answer 12

tell your math teacher that foil does not work in this case, too many terms
then ask what "simplify" means in this context
what it really means is "multiply" there is no such mathematical operation as "simplify"

Answer 13

\[
(\overbrace{\overbrace{\color{orange}a
+\underbrace{\color{cornflowerblue}b)(\color{seagreen}c}_{\text{Inside}}}^{\text{First}}
+\color{brown}d}^{\text{Outside}})
=%unklerhaukus
\overbrace{\color{orange}a\color{seagreen}c}^\text F
+\overbrace{\color{orange}a\color{brown}d}^\text O
+\underbrace{\color{cornflowerblue}b\color{seagreen}c}_\text I
+\underbrace{\color{cornflowerblue}b\color{brown}d}_\text L\\
\qquad\quad \underbrace{\qquad\qquad}_{\text{Last}}\]

\[(\color{orange}y\color{cornflowerblue}{-3}) (\color{seagreen}{2y^3-4y}+\color{brown}5)
=\overbrace{\color{orange}y\times(\color{seagreen}{2y^3-4y})}^{\text F}+\overbrace{\color{orange}y\times\color{brown}5}^{\text O}+\underbrace{\color{cornflowerblue}{-3}\times(\color{seagreen}{2y^3-4y})}_{\text I}+\underbrace{\color{cornflowerblue}{-3}\times \color{brown}5}_{\text L}%unklerhaukus\]