what is the length and width of the rectangle?

Question

the rectangle has an area of 70y^8+30y^6 square meters  the width of the rectangle (in meters) is equal to the greatest common monomial factor of 70y^8 and 30y^6

Answer 1

What is the GCF of 70 and 30?

 

70 = 2(5)(7)

30 = 2(3)(5)

 

What do they have in common? 2(5) = 10

 

70 = 10(7)

30 = 10(3)

 

What about y⁸ and y⁶?

 

y⁸ = y(y)(y)(y)(y)(y)(y)(y)

y⁶ = y(y)(y)(y)(y)(y)

 

y(y)(y)(y)(y)(y)(y) is in common, or y⁶

 

y⁸ = y⁶(y)(y) = y⁶(y²)

y⁶ = y⁶(1)

 

70y⁸ + 30y⁶ = 10y⁶(7y² + 3)

 

Notice I didn't say 3(1). That's unnecessary.