Question

Simplify completely: the quantity 10 times x to the 6th power times y to the third power plus 20 times x to the third power times y to the 2nd power all over 5 times x to the third power times y

a.2x^9y64 + 4x^6y^3

b.2x^3y^2 + 4xy

c.2x^3y^2 + 4y^2

d.2x^3y^2 + 4y

Answer 1

10x^6y^3 +20x^3y^2
--------------------- = 2x^3y^2 +4y
5x^3y

so d. is right

Answer 2

\[(10x^6y^3 + 20x^3y^2)5x^3y\]

common in the numerator is
\[10x^3y^2\] so \[(10x^3y^2(x^3 + 2))/5x^3y\]

cancel common factors... \[2y(x^3 + 2) = 2x^3y + 4y\]