phân tích đa thức thành nhân tử
a) (a2 + b2 + ab)2 – a2b2 – b2c2 – c2a2
b)(a + b + c)2 + (a + b – c)2 – 4c2
c) (a + b)3 – (a – b)3
d)x m + 4 + xm + 3 – x - 1
e)(x + y)3 – x3 – y3
f)(x + y + z)3 – x3 – y3 – z3
g)(b – c)3 + (c – a)3 + (a – b)3
|
h)x3 + y3+ z3 – 3xyz |
|
i)(x + y)5 – x5 – y5 |
|
k)(x2 + y2)3 + (z2 – x2)3 – (y2 + z2)3 |
|
|
b: \(=\left(a+b\right)^2+2c\left(a+b\right)+c^2+\left(a+b\right)^2-2c\left(a+b\right)+c^2-4c^2\)
\(=2\left(a+b\right)^2-2c^2\)
\(=2\left(a+b+c\right)\left(a+b-c\right)\)
c: \(\left(a+b\right)^3-\left(a-b\right)^3\)
\(=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3\)
\(=6a^2b+2b^3\)
\(=2b\left(3ab+1\right)\)
e: \(\left(x+y\right)^3-x^3-y^3\)
\(=x^3+3x^2y+3xy^2+y^3-x^3-y^3\)
\(=3x^2y+3xy^2=3xy\left(x+y\right)\)
