a. x³+y³+z³-3xyz

=(x³+3x²y+3xy²+y³⁾+z³+(-3xyz-3x²y-3xy²)

=((x+y)³+z³)-3xy(x+y+z)

=(x+y+z)((x+y)^2-z(x+y)+z²)-3xy(x+y+z)

=(x+y+z)(x²+2xy+y²-zx-zy+z²-3xy)

=(x+y+z)(x²-xy+y²+z²-zx-zy)

b. (x²-8)²+36

=x⁴-16x²+64+36

=x⁴-16x²+100

=(x⁴+20x²+100)-36x²

=(x²+10)²-36x²

=(x²-6x+10)(x²+6x+10)

Chúc bạn học giỏi, k cho mình nhé!!!

a)(x+y)²-(x-y)²

=(x+y-x+y)(x+y+x-y)

=2y.2x=4xy

b)(3x+1)²-(x+1)²

=(3x+1-x-1)(3x+1+x+1)

=2x.(4x+2)

=4x(2x+1)

c) x³+y³+z³-3xyz

= (x+y)³- 3xy(x+y) +z³-3xyz

=(x+y+z)( x²+2xy+y²-xz-yz+z²)-3xy(x+y+z)

=(x+y+z)(x²+y²+z²-xy-xz-yz)

Phân tích đa thức sau thành nhân tử :

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

b) \(x^3+y^3+z^3-3xyz\)

\(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)

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

\(\left(a+b\right)^3-\left(a-b\right)^3\)

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

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

\(=6a^2b+2b^3\)

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

a/\(\left(a+b\right)^3-\left(a-b\right)^3\)

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

\(=6ab^2+2b^3\)(rút gọn hết)

b/\(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3-3xy\left(x-y\right)+z^3-3xyz\)

\(=\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\)

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

\(=\left(x+y+z\right)\left[\left(x+y+z\right)^2-3z\left(x+y\right)-3xy\right]\)

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

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

Hok tốt

\(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)

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

a)(a+b+c)³ - a³ - b^{3 -} c³

= (a+b+c-a)( a²+b²+c²+2ab+2bc+2ac-a²-ab-ac+a²) - (b+c)(b²-bc+c²)

=(b+c)(a²+ab+ac+bc)

b) x³+y³+z³-3xyz

= (x+y)³-3xy(x+y) +z³-3xyz

= (x+y+z)(x²+y²+2xy-xz-yz+z²) - 3xy(x+y+z)

=(x+y+z)( x²+y²+z²-xy-yz-xz)

câu a chưa pt hết kìa :V
a, 3(a+b)(b+c)(c+a)
có thẻ dùng hđt : (a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(c+a)

\(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)

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

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

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

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

\(=\left(b+c\right)\left[a^2+b^2+c^2+a^2+a^2+2ab+2bc+2ac+ab+ac-b^2+bc-c^2\right]\)

\(=\left(b+c\right)\left(3a^2+3ab+3bc+3ac\right)\)

\(=3\left(b+c\right)\left(a+b\right)\left(a+c\right)\)

b: \(=\left(2x+2y+2z\right)^3-\left(x+y\right)^3-\left[\left(y+z\right)^3+\left(x+z\right)^3\right]\)

\(=\left(x+y+2z\right)\left[\left(2x+2y+2z\right)^2+2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\right]-\left(x+y+2z\right)\left[\left(y+z\right)^2-\left(y+z\right)\left(x+z\right)+\left(x+z\right)^2\right]\)

\(=3\left(x+y+2z\right)\left(x+z+2y\right)\left(y+z+2x\right)\)

dễ ợt

a. x^36 - 64 = (x^18)^2 - 8^2 rồi áp dụng hằng đẳng thức số 3 . câu b tương tự

thì 2 câu trên cho dễ vậy để mọi người chú ý 

chứ quan trọng là 2 câu cuối kia kìa 

tuổi con HN là :

50 : ( 1 + 4 ) = 10 ( tuổi )

tuổi bố HN là :

50 - 10 = 40 ( tuổi )

hiệu của hai bố con ko thay đổi nên hiệu vẫn là 30 tuổi

ta có sơ đồ : bố : |----|----|----|

                  con : |----| hiệu 30 tuổi

tuổi con khi đó là :

 30 : ( 3 - 1 ) = 15 ( tuổi )

số năm mà bố gấp 3 tuổi con là :

 15 - 10 = 5 ( năm )

       ĐS : 5 năm

mình nha

\(\left(3x+1\right)^2-\left(3x-1\right)^2\)

\(=\left(3x+1-3x+1\right)\left(3x+1+3x-1\right)\)

\(=2\cdot6x\)

\(=12x\)

_________

\(\left(x+y\right)^2-\left(x-y\right)^2\)

\(=\left(x+y+x-y\right)\left(x+y-x+y\right)\)

\(=2x\cdot2y\)

\(=4xy\)

\(\left(x+y\right)^3+\left(x-y\right)^3\)

\(=\left(x+y+x-y\right)\left[\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)

\(=2x\cdot\left(x^2+2xy+y^2-x^2+y^2+x^2-2xy+y^2\right)\)

\(=2x\cdot\left(x^2+3y^2\right)\)

______

\(x^3+y^3+z^3-3xyz\)

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