Answer:
Step-by-step explanation:
a) (x - y)(3y² + xy + y²)= x*(3y² + xy + y²) - y*(3y² + xy + y²)
= x*3y² + x*xy + x*y² - y* 3y² - y* xy + y² - y*y²
= 3xy² + x²y + xy² - 3y³ - xy² - y³
= 3xy² + x²y + xy² - xy²- 3y³ - y³ { xy² and - xy² will get cancelled}
=3xy² + x²y - 3y³ - y³
b)(a² - 2a + 1)(a² + 5a +6) = a²*(a² + 5a +6) - 2a(a² + 5a +6) + 1*(a² + 5a +6)
= a²*a² + a²* 5a +a²*6 - 2a*a² -2a* 5a -2a *6 + a² + 5a +6
= a⁴ + 5a³ + 6a² - 2a³ - 10a² - 12a + a² + 5a +6
= a⁴ + 5a³ - 2a³ + 6a² - 10a² + a² - 12a + 5a + 6
= a⁴ + 3a³ -3a² - 7a + 6
c) (11s +r +t) (-7r + t² + 2s) = 11s*(-7r + t² + 2s) + r*(-7r + t² + 2s) + t*(-7r + t² + 2s)
= -77sr + 11st² + 22s² - 7r² +t²r + 2sr - 7rt + t³ + 2sr
= -77sr + 2sr + 2sr + 11st² + 22s² - 7r² + rt² - 7rt + t³
= -73sr + 11st² + 22s² - 7r² +rt² - 7rt + t³
