bài1Thực hiện phép tính:

a. (5x – 2y)(x2 – xy + 1)
= 5x.(x^2-xy+1) -2y.(x^2-xy+1)
= 5x^3-5x^2y+5x-2x^2y+4xy^2-2y
= 5x^3-7x^2y+4xy^2+5x-2y

b. (x – 1)(x + 1)(x + 2)
= (x^2-1).(x+2)
=x^2.(x+2)-(x+2)
= x^3-2x^2-x-2

c. 1/2.x2y2 (2x + y)(2x – y)

a)VT=(x−1)(x2+x+1)VT=(x−1)(x2+x+1)

=x2(x−1)+x(x−1)+(x−1)=x2(x−1)+x(x−1)+(x−1)

=x3−x2+x2−x+x−1=x3−x2+x2−x+x−1

=x3−1=VP=x3−1=VP

b)VT=(x3+x2y+xy2+y3)(x−y)VT=(x3+x2y+xy2+y3)(x−y)

=x3(x−y)+x2y(x−y)+xy2(x−y)+y3(x−y)=x3(x−y)+x2y(x−y)+xy2(x−y)+y3(x−y)

=x4−x3y+x3y−x2y2+x2y2−xy3+xy3−y4=x4−x3y+x3y−x2y2+x2y2−xy3+xy3−y4

=x4−y4

1/2x2y2(2x + y)(2x - y)

= 1/2x2y2(4x2 - y2)

= 2x4y2 - 1/2x2y4

bài3Chứng minh:

a. (x – 1)(x2 + x + 1) = x3 – 1
= x.(x^2+x+1)-*x^2+x+1)
=x^3+x^2+x-x^2-x-1
=x^3-1
=> đpcm

b. (x3 + x2y + xy2 + y3)(x – y) = x4 – y4

bài 3

lỡ tay viết cái dấu mũ ra ngoài =))

a)VT=(x−1)(x2+x+1)VT=(x−1)(x2+x+1)

=x2(x−1)+x(x−1)+(x−1)=x2(x−1)+x(x−1)+(x−1)

=x3−x2+x2−x+x−1=x3−x2+x2−x+x−1

=x3−1=VP=x3−1=VP

a. (5x – 2y)(x2 – xy + 1)
= 5x.(x^2-xy+1) -2y.(x^2-xy+1)
= 5x^3-5x^2y+5x-2x^2y+4xy^2-2y
= 5x^3-7x^2y+4xy^2+5x-2y

b. (x – 1)(x + 1)(x + 2)
= (x^2-1).(x+2)
=x^2.(x+2)-(x+2)
= x^3-2x^2-x-2

c. 1/2.x2y2 (2x + y)(2x – y)