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
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