Question

A cube has a side length x and an each dimension is being increased by y, guys. :)

A). Write an expression for the surface area of the new cube, and then expand, and simplify, guys. :)
B). Please find the difference of the surface areas of the new cube and the original cube, guys. :)

Answer 1

Surface area of old cube

• 6(side)²
• 6x²

Side of new cube

• x+y

Surface area

• 6(x+y)²
• 6(x²+y²+2xy)
• 6x²+6y²+12xy

Difference

• 6y²+12xy

Answer 2

A) 6(x + y)² = 6x² + 12xy +6y²

B) 12xy +6y²

Explanation:

Surface area of a cube = 6s² (where s is the side length)

Part A

Given:

• x = side length of original cube

⇒ Surface area of the original cube = 6x²

If the side length of the cube is increased by y, then:

• (x + y) = side length of new cube

⇒ Surface area of the new cube = 6(x + y)²

Expand and simplify:

⇒ 6(x + y)²

⇒ 6(x + y)(x + y)

⇒ 6(x² + xy + xy + y²)

⇒ 6x² + 12xy +6y²

Part B

To find the difference between the surface areas of the new and original cubes, subtract the surface area of the original cube from the surface area of the new cube:

⇒ SA of new cube - SA of original cube

⇒ 6x² + 12xy +6y² - 6x²

⇒ 12xy +6y²