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Find the quotient of the quantity 4 times x to the 3rd power times y plus 12 times x to the 2nd power times y to the 3rd power minus 20 times x times y all over 4 times x times y. x2 + 3xy2 + 5
x2 + 3xy − 5
4x3y + 12x2y3 − 5
x2 + 3xy2 − 5

Respuesta :

HomertheGenius
We have to find the quotient :
( 4 x³ y + 12 x² y³ - 20 x y ) / ( 4 x y ) =
= 4 x y ( x² + 3 x y² - 5 ) / ( 4 x y ) =   ( Then 4 x y will be cancelled )
= x² + 3 x y² - 5
Answer:
 D ) x² + 3 x y² - 5

Answer:

The quotient is:

[tex]x^2+3xy^2-5[/tex]

Step-by-step explanation:

We have to find the quotient of the algebraic quantity:

[tex]\dfrac{4x^3y+12x^2y^3-20xy}{4xy}[/tex]

i..e we have dividend as:

[tex]4x^3y+12x^2y^3-20xy[/tex] , divisor as: [tex]4xy[/tex]

Now we can write our dividend term as:

[tex]4x^3y+12x^2y^3-20xy=4xy(x^2+3xy^2-5)[/tex]

Hence, the we can represent our expression as:

[tex]\dfrac{4x^3y+12xy^3-20xy}{4xy}=\dfrac{4xy(x^2+3xy^2-5)}{4xy}\\\\=x^2+3xy^2-5[/tex]

Hence, the quotient is:

[tex]x^2+3xy^2-5[/tex]

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