Simplify ( 3 x 2 + 5 y 2 ) ( 4 x y − 5 y ) . Options: A . &nbsp ( 6 x 3 y − 15 x y + 20 x y 3 − 5 y 3 ) B . &nbsp ( 12 x 3 y − 5 x 2 y + 10 x y 3 + 25 y 3 ) C . &nbsp ( 12 x 3 y − 15 x 2 y + 20 x y 3 − 25 y 3 ) D . &nbsp ( 6 x 3 y − 15 x 2 y + 10 x y 3 − 5 y 3 )

Simplify (3x2+5y2)(4xy−5y).

Question

Simplify $(3 x^{2} + 5 y^{2}) (4 x y - 5 y)$ .

Options:

A .

(6 x^{3} y - 15 x y + 20 x y^{3} - 5 y^{3})

B .

(12 x^{3} y - 5 x^{2} y + 10 x y^{3} + 25 y^{3})

C .

(12 x^{3} y - 15 x^{2} y + 20 x y^{3} - 25 y^{3})

D .

(6 x^{3} y - 15 x^{2} y + 10 x y^{3} - 5 y^{3})

Answer: Option C
:
C

Given: $(3 x^{2} + 5 y^{2}) (4 x y - 5 y)$
$= 3 x^{2} (4 x y - 5 y) + 5 y^{2} (4 x y - 5 y)$
$= 12 x^{3} y - 15 x^{2} y + 20 x y^{3} - 25 y^{3}$

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