Answer:
Option 4th is correct
[tex]2x^3y^2+4y[/tex]
Step-by-step explanation:
GCF(Greatest common factor) is the largest number that divide the polynomial.
Given the statement:
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
⇒[tex]\frac{10x^6y^3+20x^3y^2}{5x^3y}[/tex]
To simplify this expression:
GCF of [tex]10x^6y^3[/tex] and [tex]20x^3y^2[/tex] is, [tex]10x^3y^2[/tex]
then;
[tex]\frac{10x^3y^2(x^3y+2)}{5x^3y}[/tex]
⇒[tex]2y(x^3y+2)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
⇒[tex]2x^3y^2+4y[/tex]
Therefore, the simplified expression is, [tex]2x^3y^2+4y[/tex]
