Question

Let the polynomials A = 7x² + 3xy and B = -3xy .

Determine A. B (multiplication)


a) - 21x 2 – 9xy

b) 21x 2 + 9xy

c) – 7x 2 – 3xy

d) 7x 3 + 3x 2 y 2

e) – 21x 3 y – 9x 2 y 2

Answer 1

– 21x^3 y – 9x^2 y^2 e) is your answer

Explanation:

Solve the following system for A and B:

{A = 7 x^2 + 3 x y

B = -3 x y

Express the system in matrix form:

(1 | 0

0 | 1)(A

B) = (7 x^2 + 3 x y

-3 x y)

Write the system in augmented matrix form and use Gaussian elimination:

(1 | 0 | 7 x^2 + 3 x y

0 | 1 | -3 x y)

Collect results:

Answer: {A = 7 x^2 + 3 x y , B = -3 x y

then we multiply the results (7 x^2 + 3 x y) ( -3 x y) = – 21x^3 y – 9x^2 y^2