Question

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} + x^{m + 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

Answer 1

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: \(\left(x+y\right)^3-x^3-y^3\)

\(=x^3+3x^2y+3xy^2+y^3-x^3-y^3\)

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