Answer:
Option 4th is correct
\(2x^3y^2+4y\)
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
⇒\(\frac{10x^6y^3+20x^3y^2}{5x^3y}\)
To simplify this expression:
GCF of \(10x^6y^3\) and \(20x^3y^2\) is, \(10x^3y^2\)
then;
\(\frac{10x^3y^2(x^3y+2)}{5x^3y}\)
⇒\(2y(x^3y+2)\)
Using distributive property: \(a\cdot (b+c) = a\cdot b+ a\cdot c\)
⇒\(2x^3y^2+4y\)
Therefore, the simplified expression is, \(2x^3y^2+4y\)
