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.

2x9y4 + 4x6y3
2x3y2 + 4xy
2x3y2 + 4y2
2x3y2 + 4y

Answer 1

(10x^6y^3 + 20x^3y^2) / 5x^3y

10x^6y^3 / 5x^3y ⇒ 2x^3y^2
20x^3y^2 / 5x^3y ⇒ 4y

2x³y² + 4y This is the simplified answer. The last option.

Answer 2

Option 4th is correct

`2x^3y^2+4y`

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

⇒
`(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;

`(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`