Question

bai1: rut gon cac bieu thuc sau

a, (2x-y).(4x^2+2xy+y^2)-(2x+y).(4x^2-2xy+y^2)

b, (3x+2y).(9x^2-6xy+4y^2)-27x^3

c,8x.(x-2y).(x+2y)+(y-2x).(x^2+2xy+4x^2)

bai2 :cmr

a, a^3+b^3=(a+b)^3-3ab.(a+b)

b.a^3-b^3=(a-b)+3ab,(a-b)

Answer 1

bai2 :cmr

a, a^3+b^3=(a+b)^3-3ab.(a+b)

VP= \(\left(a+b\right)^3-3ab\left(a+b\right)\)

=\(a^3+b^3+3a^2b+3ab^2-3a^2b-3ab^2=a^3+b^3\)

=VT

b.a^3-b^3=(a-b)^3+3ab,(a-b)

\(VP=\left(a-b\right)^3+3ab\left(a-b\right)\)

=\(a^3-3a^2b+ab^2.3-b^3+3a^2b-3ab^2=a^3-b^3\)

=VT

=> ĐPCM

 

Answer 2

bài 1.

a) = 8x^3+4x^2y+2xy^2-4x^2y-2xy^2-y^3-(8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3)

= 8x³+4x_²y+2xy_²-4x²y-2xy²-y³ - 8x³+4x²y-2xy²-4x²y+2xy²-y³

=-8x²y-6y³

b) = 27x³-18x²y+12xy²+18x²y-12xy²+8y³-27x³

=8y