Kaspaueru2

2021-12-16

Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
(2x+3y)(x-y)

accimaroyalde

Step 1
FOIL method:
Step 2
(2x+3y)(x-y)
multiplication using FOIL method:
= (2x)(x) + (2x)(-y) + (3y)(x) + (3y)(-y)
$=2{x}^{2}-2xy+3xy-3{y}^{2}$
$=2{x}^{2}+xy-3{y}^{2}$

polynomial in standard form:
$\left(2x+3y\right)\left(x-y\right)=2{x}^{2}+xy-3{y}^{2}$

lalilulelo2k3eq

Multiply the terms of the polynomials in the order First, Outer, Inner and Last.
$\left(2x+3y\right)\left(x-y\right)=2x\cdot x+2x\left(-y\right)+3y\cdot x+3y\left(-y\right)$
Use the laws of exponents to multiply the monomials.
$2x\cdot x+2x\left(-y\right)+3y\cdot x+3y\left(-y\right)=2{x}^{1+1}-2xy+3xy-3{y}^{1+1}$
$=2{x}^{2}-2xy+3xy-3{y}^{2}$
Now, combine the like terms using the distributive property.
$2{x}^{2}-2xy+3xy-3{y}^{2}=2{x}^{2}+\left(-2+3\right)xy-3{y}^{2}$
$=2{x}^{2}+xy-3{y}^{2}$
Therefore, the product is $2{x}^{2}+xy-3{y}^{2}$.

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