Question

PLEASE HELP!!!!!! what is the simplified expression to represent the area of the shaded region???

Answer 1

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