Câu 1 :
a) (x + 3)(x 2 + 3x – 5)
= x.(x 2 + 3x – 5) + 3.(x 2 + 3x – 5)
= x.x 2 + x.3x + x.(–5) + 3.x 2 + 3.3x + 3.(–5)
= x 3 + 3x 2 – 5x + 3x 2 + 9x – 15
= x 3 + (3x 2 + 3x 2 ) + (9x – 5x) – 15
= x 3 + 6x 2 + 4x – 15.
b) (xy – 1)(xy + 5)
= xy.(xy + 5) + (–1).(xy + 5)
= xy.xy + xy.5 + (–1).xy + (–1).5
= x 2 y 2 + 5xy – xy – 5
= x 2 y 2 + 4xy – 5.
Câu 2 :
( xy – 1).(x 3 – 2x – 6) = xy.(x 3 – 2x – 6) + (-1).(x 3 – 2x – 6)
= xy.x 3 + xy.(-2x) + xy.(-6) + (-1).x 3 + (-1).(-2x) + (-1).(-6)
= x (1 + 3) y - x (1 + 1) y - 3xy - x 3 + 2x + 6
= x 4 y-x 2 y - 3xy - x 3 + 2x + 6
= x 4 y - x 3 - x 2 y - 3xy + 2x + 6
