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There is a rectangle, it's height is 3x and its width is 2x+xy. Find the area, but in the rectangle there are to empty boxes, there width and hight are x.

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1 Answer

Hi Shivansh,
 
Step 1. If you draw a rectangle, you can label the height as 3x and the width as 2x+xy.  
 
Step 2. The area of the large rectangle is height multiplied by the width: 3x(2x + xy).  You can use the distributive property to simplify the terms: 3x(2x) + 3x(xy) = 6x2 + 3x2y .
 
Step 3. To find the area of the two smaller boxes inside the rectangle, draw a line that separates the width into two parts, so that one part will have a width of 2x and the other part will have a width of xy.  The height, 3x, remains the same for both of the smaller boxes.
 
Therefore the area of the two boxes will be:
3x(2x) = 6xand 3x(xy) = 3x2y, which are identical to the terms created when we distributed in step 2.
 
Hope that helps.
 
 
 

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You're welcome, and yes, the area of the large rectangle is both terms together: 6x2 + 3x2y . 

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