1. Find the area of the shaded region. Express it in factored form.
2. Express the area and perimeter of the shaded in factored form.

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1
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2014-07-18T00:19:46+08:00

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1) Area of larger region = (3x-5)(3x-5) 
   Area of smaller region =  (x+1)(x+1)
 
Subtract area of smaller region from area of larger region:

 (3x-5)(3x-5) - (x+1)(x+1)

9x^2 -30x +25 - (x^2+2x+1) = 9x^2 -30x +25 -x^2-2x-1

8x^2 -32x +24 = 8(x^2-4x+3)

\boxed{8(x-3)(x-1)}



2) Length of shaded region = a³ - b³
    Width of shaded region = a² + ab +b²

Perimeter=2(l + w)=2(a^3-b^3+a^2+ab+b^2)

(But a^3-b^3= (a-b)(a^2+ab+b^2) )

So, 2(a^3-b^3+a^2+ab+b^2) = 2[(a-b)(a^2+ab+b^2)+(a^2+ab+b^2)]

Final factored form for perimeter = \boxed{2(a^2+ab+b^2)(a-b+1)}


Area = l\times w= (a^3-b^3)(a^2+ab+b^2)

(But a^3-b^3= (a-b)(a^2+ab+b^2) )

So, the final factored form for Area = \boxed{(a-b)(a^2+ab+b^2)^2}
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