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Alona [7]
1 year ago
5

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the pairs of polynomials to their products.

(xy + 9y + 2) and (xy – 3) x2y2 + 3x2y – 7xy – 27x – 18 (2xy + x + y) and (3xy2 – y) 6x2y3 – 2xy2 + 3x2y2 – xy + 3xy3 – y2 (x – y) and (x + 3y) x3y + 3x2 + 3x2y2 + 7xy – 6 (xy + 3x + 2) and (xy – 9) x2 – 9y2 (x2 + 3xy – 2) and (xy + 3) (x + 3y) and (x – 3y)
Mathematics
1 answer:
andreyandreev [35.5K]1 year ago
5 0

The products of the polynomials are:

  • (xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6
  • (2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²
  • (x - y) * (x + 3y) = x² + 2xy + 3y²
  • (xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18
  • (x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6
  • (x + 3y) * (x – 3y) = x² - 9y²

<h3>How to evaluate the products?</h3>

To do this, we multiply each pair of polynomial as follows:

<u>Pair 1: (xy + 9y + 2) and (xy – 3)</u>

(xy + 9y + 2) * (xy - 3)

Expand

(xy + 9y + 2) * (xy - 3) = x²y² - 3xy + 9xy² - 27y + 2xy - 6

Evaluate the like terms

(xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6

<u>Pair 2: (2xy + x + y) and (3xy² - y)</u>

(2xy + x + y) * (3xy² - y)

Expand

(2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²

<u>Pair 3: (x – y) and (x + 3y) </u>

(x - y) * (x + 3y)

Expand

(x - y) * (x + 3y) = x² + 3xy - yx + 3y²

Evaluate the like terms

(x - y) * (x + 3y) = x² + 2xy + 3y²

<u>Pair 4: (xy + 3x + 2) and (xy – 9) </u>

(xy + 3x + 2) * (xy – 9)

Expand

(xy + 3x + 2) * (xy – 9)  = x²y² - 9xy + 3x²y - 27x + 2xy - 18

Evaluate the like terms

(xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18

<u>Pair 5: (x² + 3xy - 2) and (xy + 3) </u>

(x² + 3xy - 2) * (xy + 3)

Expand

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 9xy - 2xy - 6

Evaluate the like terms

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6

<u>Pair 6: (x + 3y) and (x – 3y)</u>

(x + 3y) * (x – 3y)

Apply the difference of two squares

(x + 3y) * (x – 3y) = x² - 9y²

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

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VARVARA [1.3K]

Answer:

6x² – 10y² + 2xy + 10

Step-by-step explanation:

We'll begin calculating the sum of

x² + 3y² – 6xy and 2x² – y² + 8xy + 8

This can be obtained as follow:

... x² + 3y² – 6xy

+ 2x² – y² + 8xy + 8

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

3x² – 2y² + 2xy + 8

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Next, we shall determine the sum of:

–3x² + 4y² + 3 and 4y² – 5

This can be obtained as follow:

–3x² + 4y² + 3

+ 4y² – 5

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

–3x² + 8y² – 2

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Finally, we shall subtract the sum of:

–3x² + 4y² + 3 and 4y² – 5

from the sum of:

x² + 3y² – 6xy and 2x² – y² + 8xy + 8

This can be obtained as follow:

.. 3x² – 2y² + 2xy + 8

– (–3x² + 8y² – 2)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

6x² – 10y² + 2xy + 10

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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