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scZoUnD [109]
2 years ago
11

Product of (x+y+2)(y+1)

Mathematics
1 answer:
andre [41]2 years ago
6 0

Answer: x ( y + 1) + y ( y + 3) + 2

Step-by-step explanation:

( x + y + 2) ( y + 1)

x ( y + 1) + y ( y + 1) + 2 ( y + 1)

expanding the bracket

( xy + x) + ( y2 + y) + ( 2y + 2)

removing the bracket

xy + x + y2 +y + 2y + 2

collecting like terms

xy + x + y2 + 3y + 2

given as: x(y + 1) + y ( y + 3) + 2

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a. Find the graph of their common region in the attachment

b. The area of the common region of the graphs is 8 units²

<h3>a. How to sketch the region common to the graphs?</h3>

Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.

  • The graph of x ≥ 2 is the region right of the line x = 2.
  • The graph of y ≥ 0 is the region above the line y = 0 or x-axis.
  • To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.

So, the graph of x + y ≤ 6 is the region below the line y = - x + 6

From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)

Find the graph of their common region in the attachment

<h3>b. The area of the common region</h3>

From the graph, we see that the common region is a right angled triangle with

  • height = 4 units and
  • base = 4 units

So, its area = 1/2 × height × base

= 1/2 × 4 units × 4 units

= 1/2 × 16 units²

= 8 units²

So, the area of the common region of the graphs is 8 units²

Learn more about region common to graphs here:

brainly.com/question/27932405

#SPJ1

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