Answer:
The width of the rectangle with area 70y⁸+ 30y⁶is 10y⁶.
The length of the rectangle with area 70y⁸+ 30y⁶ is (7y²+3).
Step-by-step explanation:
Monomial: Monomial is an algebraic expression which is consisting of only one term.
Binomial: Binomial is an algebraic expression which is consisting of two terms.
Trinomial: Trinomial is an algebraic expression which is consisting of three terms.
The area of a rectangle is= Length× width
Given that,
The area of the rectangle is
=70y⁸+30y⁶
70y⁸=7×5×2×y×y×y×y×y×y×y×y
30y⁶=5×3×2×y×y×y×y×y×y
The common factors of 70y⁸ and 30y⁶ are = 5,2,y,y,y,y,y,y
The greatest common factor of 70y⁸ and 30y⁶ is
=5×2×y×y×y×y×y×y
=10y⁶
∴70y⁸+ 30y⁶
= 10y⁶(7y²+3)
The greatest common monomial of 70y⁸+ 30y⁶ is 10y⁶.
Given that,
The greatest common monomial factor of 70y⁸+ 30y⁶ is equal to the width of the rectangle.
The width of the rectangle with area 70y⁸+ 30y⁶is 10y⁶.
Then the length of the rectangle with area 70y⁸+ 30y⁶ is (7y²+3).
[ area = length × width]
