A portrait without its frame has a height of 2.5 times its width w, in inches. Its frame is 2 in. Wide all along its perimeter. What is an expression for the area of the framed portrait in terms of w? Simplify your expression & write it in standard form. Fill in the blanks:

2.5w² + 14w + 16

Step-by-step 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

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step-by-step explanation: