Lincoln Hernandez

2022-02-03

How do you foil (6x-y)(3x-2y)?

Nathen Lamb

Add (product of F rst terms) plus (product of O utside terms) plus (product of I nside terms) plus (product of L ast terms) to get
$18{x}^{2}-15xy+2{y}^{2}$
Explanation:
First terms: 6x and 3x
Product of First terms: $18{x}^{2}$
Outside terms: 6x and 3x
Product of Outside terms : -12xy
Inside terms: -y and 3x
Product of Inside terms: -3xy
Last terms: -y and -2y
Product of Last terms: $2{y}^{2}$
Sum of Products:
$18{x}^{2}-12xy-3xy+2{y}^{2}$
$=18{x}^{2}-15xy+2{y}^{2}$

Evie French

Explanation:
When we multiply two polynomials, we must multiply each (and every) term in one times each (and every) term of the other.
{Reminder: things that are to be multiplied are called "factors", things to be added are called "terms".)
Many people use FOIL to remind themselves and to keep track of how to multiply these:
Multiply: (6x-y)(3x-2y) (in this example we'll use FOIL)
First $\left(6x-y\right)\left(3x-2y\right)\left(6x\right)\left(3x\right)=18{x}^{2}$
Outside (6x-y)(3x-9) (6x)(-2y)=-12xy
Inside (6x-y)(3x-2y) (-y)(3x)=-3xy
Last $\left(6x-y\right)\left(3x-2y\right)\left(-y\right)\left(-2y\right)=2{y}^{2}$
Written on one line, we have:
(6x-y)(3x-2y)=(6x)(3x)+(6x)(-2y)+(-y)(3x)+(-y)(-2y)
$\left(6x-y\right)\left(3x-2y\right)=18{x}^{2}-12xy-3xy+2{y}^{2}$ now combine similar terms
$\left(6x-y\right)\left(3x-2y\right)=18{x}^{2}-15xy+2{y}^{2}$

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