Select the correct answer from each drop-down menu.A rope is cut into three pieces. The lengths are given as 2ab(a − b), 3a2(a + 2b), and b2(2a − b).The expression representing the total length of the rope is .If a = 2 inches and b = 3 inches, the total length of the rope is inches.math
Accepted Solution
A:
Answer: 1) [tex]3 a^3 + 8 a^2 b - b^3[/tex] 2) 93 inches Step-by-step explanation: 1) We know that the lenghts are given by these expressions: [tex]2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)[/tex] Then, we need to add them in order to find the expression that represents the total length of the rope: - Apply Distributive property. - Add the like terms. Then: [tex]=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3[/tex] 2) Knowing that: [tex]a=2in\\\\b=3in[/tex] We must substitute these values into [tex]3 a^3 + 8 a^2 b - b^3[/tex] in order to caculate the total lenght of the rope. This is: [tex]3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in[/tex]