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yarubiks

The original area of a face would be a^2. Now that you added b to the edge, the new area of each face would be (a+b)^2. To find how much the are increased, subtract a^2 from (a+b)^2. [tex] (a+b)^2-(a^2)= a^2+2ab+b^2-(a^2)= 2ab+b^2= b(2a+b) [/tex] So the answer is b(2a+b)

Volume of the cube = a³ (Given)

[tex] \boxed{ \text{Volume of a cube = side}^3} [/tex]

Side of a cube = ∛a³ = a

Side of the cube after it increased by b = a + b

[tex] \boxed{\text{Area of a cube = side}^2} [/tex]

Area of the cube = (a + b)²

Increase in area = (a + b)² - a²

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Simplify (a + b)² - a²:

(a + b)² - a²

Open (a + b)² as a² + 2ab + b² :

= a² + 2ab + b² - a²

Combine a² and -a²:

= 2ab + b²

Take out b as the common factor:

= b(2a + b)

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Answer: (H) b(2a + b)

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