\(A=\left(a+b+c\right)^3+\left(a-b-c\right)^3-6a\left(b+c\right)^2\)

\(=\left[a+\left(b+c\right)\right]^3+\left[a-\left(b+c\right)\right]^3-6a\left(b+c\right)^2\)

\(=a^3+3a^2\left(b+c\right)+3a\left(b+c\right)^2+\left(b+c\right)^3+a^3-3a^2\left(b+c\right)+3a\left(b+c\right)^2-\left(b+c\right)^3-6a\left(b+c\right)^2\)

\(=2a^3\)

Đặt x = a+b , y = b+c , z = c+a

Thì biểu thức trên trở thành \(x^3+y^3+z^3-3xyz=\left(x+y\right)^3+z^3-3xy-3xyz\)

\(=\left(x+y+z\right)\left(x^2+y^2+2xy-xz-yz+z^2\right)-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

Từ đó thay a,b,c vào rồi rút gọn :)

 bạn tham khảo link này nhé:

https://olm.vn/hoi-dap/detail/101383958371.html

#hok tốt#

\(\left(a+b+c\right)^3+\left(a-b-c\right)^3-6a\left(b+c\right)^2\)

\(=a^3+b^3+c^3+a^3-b^3-c^3-6a\left(b^2+c^2\right)\)

\(=\left(a^3+a^3\right)+\left(b^3-b^3\right) +\left(c^3-c^3\right)-6a\left(b^2+c^2\right)\)

\(=2a^3-6a\left(b^2+c^2\right)\)

\(=2a^2\cdot a-6a\left(b^2+c^2\right)\)

\(=a\left[2a^2-6\left(b^2+c^2\right)\right]\)

\(\text{Chắc là vậy !}\)

Link nè :

https://olm.vn/hoi-dap/detail/101383958371.html

k mk nhé mk hông giải nên mk cho bn link rùi nè

Ta có: A=(a+b+c)3+(a−b−c)3−6a(b+c)2 

= a^3  + b^3 + c^3 + 3ab + 3ac + 3bc + a^3 + b^3 + c^3 - 3ab - 3ac + 3bc - 6a(b^2+2bc + c^2)

= a^3  + b^3 + c^3 + 3ab + 3ac + 3bc + a^3 + b^3 + c^3 - 3ab - 3ac + 3bc - 6ab^2 + 12abc+6ac^2

=2a^3 + 2b^3 + 2c^3 + 6a^2 + 12abc

Cậu dùng hằng đẳng thức nâng cao là ra. Nhớ tick mình nha,

a) ( x - 5 )( 2x + 3 ) + 2x( 1 - x )

= 2x² - 7x - 15 + 2x - 2x²

= -5x - 15

= -5( x + 3 )

b) ( 3x - 5 )² - ( x + 5 )( 5 - x ) - 5/2( -2x )²

= 9x² - 30x + 25 + ( x + 5 )( x - 5 ) - 5/2.4x²

= 9x² - 30x + 25 + x² - 25 - 10x²

= -30x

c) ( 3x + 2 )( 4 - 6x + 9x² ) - 3x( 3x - 2 )² + 12( -2/3 - 3x² )

= ( 3x )³ + 2³ - 3x( 9x² - 12x + 4 ) - 8 - 36x²

= 27x³ + 8 - 27x³ + 36x² - 12x - 8 - 36x²

= -12x

a, \(\left(x-5\right)\left(2x+3\right)+2x\left(1-x\right)=2x^2+3x-10x-15+2x-2x^2=-5x-15\)

b, \(\left(3x-5\right)^2-\left(x+5\right)\left(5-x\right)-\frac{5}{2}\left(-2x\right)^2\)

\(=9x^2-30x+25-\left(5x-x^2+25-5x\right)-\frac{5}{2}\left(4x^2\right)\)

\(=-30x\)

Đặt b+c=x ta được:

A=(a+x)³+(a-x)³-6a.x²

=a³+3a²x+3ax²+x³+a³-3a²x+3ax²-x³-6ax²

=2a³