Đáp án:
Giải thích các bước giải:
Bài 1:
a) 2x.(x^2 - 7x - 3)
= 2x^3 - 14x^2 - 6x
b) (-2x^3 + 3/4.y^2 - 7xy). 4xy^2
= -8.x^4.y^2 + 3.x.y^4 - 28.x^2.y^3
c) (-5x^3) . (2x^2 + 3x - 5)
= -10x^5 - 15x^4 + 25x^3
d) (2x^2 - 1/3.xy + y^2) . (-3x^3)
= -6x^5 + x^4.y - 3.x^3.y^2
e) (x^2 - 2x + 3) . (x - 4)
= x^3 - 2x^2 + 3x - 4x^2 + 8x - 12
= x^3 - (2x^2 + 4x^2) + (3x + 8x) - 12
= x^3 - 6x^2 + 11x - 12
f) (2x^3 - 3x - 1) . (5x + 2)
= 10x^4 - 15x^2 - 5x + 4x^3 - 6x - 2
= 10x^4 + 4x^3 - 15x^2 - (5x + 6x) - 2
= 10x^4 + 4x^3 - 15x^2 - 11x - 2
g) (25x^2 + 10xy + 4y^2) . (5x - 2y)
= 125x^3 + 50.x^2.y + 20.x.y^2 - 50.x^2.y - 20.x.y^2 - 8y^3
= 125x^3 + (50.x^2.y - 50.x^2.y) + (20.x.y^2 - 20.x.y^2) - 8y^3
= 125x^3 - 8y^3
h) (5x^3 - x^2 + 2x - 3) . (4x^2 - x + 2)
= 20x^5 - 4x^4 + 8x^3 - 12x^2 - 5x^4 + x^3 -2x^2 + 3x + 10x^3 - 2x^2 + 4x - 6
= 20x^5 + (-4x^4 - 5x^4) + (8x^3 + x^3 + 10x^3) + (-12x^2 - 2x^2 - 2x^2) + (3x + 4x) - 6
= 20x^5 - 9x^4 + 19x^3 - 16x^2 + 7x -6
Bài 2:
a) (2x + 3y)^2 = 4x^2 + 12xy + 9y^2
b) (5x - y)^2 = 25x^2 - 10xy + y^2
c) (2x + y^2)^3 = 8x^3 + 12x^2y^2 + 6xy^4 + y^5
d) (3x^2 - 2y)^3 = 27x^6 - 54.x^4.y + 36.x^2.y^2 - 8y^3
e) (x + 4).(x^2 - 4x + 16)
= x^3 - 4x^2 + 16x + 4x^2 - 16x + 64
= x^3 + (-4x^2 + 4x^2) + (16x - 16x) + 64
= x^3 + 64
h) (x - 3y).(x^2 + 3xy + 9y^2)
= x^3 + 3.x^2.y + 9.x.y^2 - 3.x^2.y - 9.x.y^2 - 27y^3
= x^3 + (3.x^2.y - 3.x^2.y) + (9.x.y^2 - 9.x.y^2) - 27y^3
= x^3 - 27y^3
d) (x^2 + 2/5.y) . (x^2 - 2/5.y) = x^4 - 4/25.y^2
