Find a polynomial expression for the surface area of the cube.
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Area of a square: ( x + 3 ) ( x + 3 ) = ( x + 3 ) 2 Using the identity ( x + y ) 2 = x 2 + 2 x y + y 2 ⟹ = x 2 + 6 x + 9
There are 6 squares so: 6 × ( x 2 + 6 x + 9 ) ⟹ 6 x 2 + 3 6 x + 5 4
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Each face of the cube is a square of length ( x + 3 )
The area of each square,
= ( x + 3 ) ( x + 3 )
= x ( x + 3 ) + 3 ( x + 3 )
= x 2 + 3 x + 3 x + 9
= x 2 + 6 x + 9
Now,
The cube has six such faces
The total surface area of the cube,
= 6 × The area of one face
= 6 ( x 2 + 6 x + 9 )
= 6 x 2 + 3 6 x + 5 4