Answer: 29x+23
Step-by-step explanation:
In order to find the area of the shaded region, we need to subtract the unshaded region in middle from the large rectangle
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Step 1. Find the area of the large rectangle
A=lw (length × width)
A=(2x+4)(3x+6)
A=6x²+12x+12x+24 ⇔ Use FOIL (First Outer Inner Later)
A=6x²+24x+24
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Step 2. Find the area of the unshaded region
A=lw
A=(2x-1)(3x-1)
A=6x²-2x-3x+1 ⇔ Use FOIL
A=6x²-5x+1
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Step 3. Subtract unshaded from the large rectangle to get the area of shaded region
A (shade region)=large rectangle-unshaded region
A (shade region)=(6x²+24x+24)-(6x²-5x+1)
A (shade region)=6x²+24x+24-6x²+5x-1 ⇔ get off parenthesis
A (shade region)=6x²-6x²+24x+5x+24-1 ⇔ move the like term together
A (shade region)=29x+23 ⇔ combine like term
