Question

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.

Answer 1

See below!

Explanation:

Given that,

A rope is cut into three pieces.

Given length of each piece.

• 2ab(a - b)
• 3a²(a + 2b)
• b²(2a - b)

Part 1:

To find the total length of rope, we simply have to add all the lengths of the pieces.

= 2ab(a - b) + 3a²(a + 2b) + b²(2a - b)

• Distribute

= 2a²b - 2ab² + 3a³ + 6a²b + 2ab² - b³

• Combine like terms

= 3a³ + 2a²b + 6a²b - 2ab² + 2ab² - b³

• Cancel +2ab² and -2ab²

= 3a³ + 8a²b - b³

Part 2:

Put a = 2 in., b = 3 in.

= 3(2)³ + 8(2)²(3) - (3)³

= 3(8) + 8(4)(3) - 27

= 24 + 96 - 27

= 93 inches

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