Question

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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

Answer 1

1)
`3 a^3 + 8 a^2 b - b^3`

2) 93 inches

Explanation:

1) We know that the lenghts are given by these expressions:

`2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)`

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:

`=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3`

2) Knowing that:

`a=2in\\\\b=3in`

We must substitute these values into
`3 a^3 + 8 a^2 b - b^3` in order to caculate the total lenght of the rope. This is:

`3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in`