Answer:
Left circle: 6x + 2y
Bottom middle circle: 5x
Bottom right rectangle: 3x + y
Explanation:
According to the question, the expression in each circle is the result of the sum of the two rectangles connected to it.
The expression in the left circle is the sum of the expressions in the rectangles above and below it:
⇒ (4x + 3y) + (2x - y)
⇒ 4x + 3y + 2x - y
⇒ 4x + 2x + 3y - y
⇒ 6x + 2y
Therefore, the expression in the left circle is 6x + 2y.
The expression in the right circle is the sum of the expressions in the rectangles above and below it, however the expression in the rectangle below this circle is missing.
To find the missing expression, subtract the expression in the rectangle above the circle from the expression in the circle:
⇒ (4x + 5y) - (x + 4y)
⇒ 4x + 5y - x - 4y
⇒ 4x - x + 5y - 4y
⇒ 3x + y
Therefore, the expression in the lower right rectangle is 3x + y.
The expression in the bottom middle circle is is the sum of the expressions in the rectangles to its left and right:
⇒ (2x - y) + (3x + y)
⇒ 2x - y + 3x + y
⇒ 2x + 3x - y + y
⇒ 5x
Therefore, the expression in the bottom middle circle is 5x.