Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
(x-2y)(x+y)
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Corgnatiui
Step 1
Given:
(x-2y)(x+y)
To Find:
Using FOIL method express the polynomial in standard form
Step 2
Explanation:
FOIL(First, Outer, Inner, Last)
So, $\left(x-2y\right)\left(x+y\right)={x}^{2}+xy-2xy-2{y}^{2}$
$⇒\left(x-2y\right)\left(x+y\right)={x}^{2}-xy-2{y}^{2}$
Step 3
$\left(x-2y\right)\left(x+y\right)={x}^{2}-xy-2{y}^{2}$

scoollato7o
Multiply the binomials using the FOIL method.
(x-2y)(x+y)=x*x+x*y+(-2y)x+(-2y)y
Multiply the monomials using the laws of exponents.
$x\cdot x+x\cdot y+\left(-2y\right)x+\left(-2y\right)y={x}^{1+1}+xy+\left(-2xy\right)+\left(-2{y}^{2}\right)$
$={x}^{2}+xy-2xy-2{y}^{2}$
Combine the like terms using the distributive property.
${x}^{2}+xy-2xy-2{y}^{2}={x}^{2}+\left(1-2\right)xy-2{y}^{2}$
$={x}^{2}+\left(-1\right)xy-2{y}^{2}$
$={x}^{2}-xy-2{y}^{2}$
Therefore, the result is ${x}^{2}-xy-2{y}^{2}$.