Answer:
2.5w² + 14w + 16
Explanation:
Width of portrait without frame = w
Height of portrait without frame = 2.5*w = 2.5w
Given that the portrait has a frame that is 2 in wide all along its borders, therefore,
Width of framed portrait = w + 2 + 2 = w + 4
Height of framed portrait = 2.5w + 2 + 2 = 2.5w + 4
Expression of the area of the framed portrait in terms of w = (w + 4)(2.5w + 4)
Simplify and express in standard form as follows:
Area = (w + 4)(2.5w + 4)
Apply the distributive property of multiplication
w(2.5w + 4) +4(2.5w + 4)
2.5w² + 4w + 10w + 16
Combine like terms
Area = 2.5w² + 14w + 16