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McGraw Hill Integrated II, 2012 View details

6. Solving x^2+bx+c=0

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Exercise 60 Page 51

Use the Square of a Sum Formula, (a+b)=a^2+2ab+b^2.

8d+16

Practice makes perfect

We want to write a polynomial that represents the area of the shaded region.

To do so, we need to subtract the area A_w of the white square from the area A_b of the big square. Let's write A_w and A_b. A_w= d^2 and A_b= (d+4)^2 We need to find A_b-A_w.

A_b-A_w

SubstituteExpressions

Substitute expressions

(d+4)^2- d^2

ExpandPosPerfectSquare

(a+b)^2=a^2+2ab+b^2

d^2+8d+16-d^2

SubTerms

Subtract terms

8d+16

The area of the shaded region is 8d+16.