Given:
Each circle is the result of the sum of two rectangles connected to it.
To find:
The missing expression in their simplified form.
Solution:
<u>Left side circle:</u>
Left circle = (5x + 2y) + (x + y)
= 5x + 2y + x + y
= 6x + 7y
The expression in left side circle is 6x + 7y.
<u>Right side rectangle:</u>
5x + 4y = (4x + 5y) + Right rectangle
Subtract 4x + 5y from both sides.
5x + 4y - (4x + 5y) = Right rectangle
5x + 4y - 4x - 5y = Right rectangle
x - y = Right rectangle
The expression in right side rectangle is x - y.
<u>Bottom circle:</u>
Bottom circle = (x + y) + (x - y)
= x + y + x - y
= 2x
The expression in left side circle is 2x.