Question

help me help me!!

Dùng công thức A³=A².A , chứng minh:

a) (a-b)³=-(b-a)

b) (-a-b)²= (a+b)²

^c) (x+y⁾³= x(x-3y)²+y(y-3x)²

^d) (x+y)³-(x-y)³=2y(y²+3x²)

thanks nhá.

Answer 1

Lời giải:

a)

$(a-b)^3=(a-b)^2.(a-b)=(b-a)^2.-(b-a)=-(b-a)^3$

b)

$(-a-b)^2=[-(a+b)]^2=(-1)^2(a+b)^2=(a+b)^2$
c)

$(x+y)^3=x^3+3x^2y+3xy^2+y^3$

$=x^3-6x^2y+9x^2y-6xy^2+9xy^2+y^3$

$=(x^3-6x^2y+9xy^2)+(y^3-6xy^2+9x^2y)$

$=x(x^2-6xy+9y^2)+y(y^2-6xy+9x^2)$

$=x(x-3y)^2+y(y-3x)^2$
d)

$(x+y)^3-(x-y)^3=x^3+3xy(x+y)+y^3-[x^3-3xy(x-y)-y^3]$

$=2y^3+3xy[(x+y)+(x-y)]=2y^3+6x^2y=2y(y^2+3x^2)$

Answer 2

Lời giải:

a)

$(a-b)^3=(a-b)^2.(a-b)=(b-a)^2.-(b-a)=-(b-a)^3$

b)

$(-a-b)^2=[-(a+b)]^2=(-1)^2(a+b)^2=(a+b)^2$
c)

$(x+y)^3=x^3+3x^2y+3xy^2+y^3$

$=x^3-6x^2y+9x^2y-6xy^2+9xy^2+y^3$

$=(x^3-6x^2y+9xy^2)+(y^3-6xy^2+9x^2y)$

$=x(x^2-6xy+9y^2)+y(y^2-6xy+9x^2)$

$=x(x-3y)^2+y(y-3x)^2$
d)

$(x+y)^3-(x-y)^3=x^3+3xy(x+y)+y^3-[x^3-3xy(x-y)-y^3]$

$=2y^3+3xy[(x+y)+(x-y)]=2y^3+6x^2y=2y(y^2+3x^2)$