Question

Phân tích đa thức thành nhân tử

a) \(x^2-y^2-2x+2y\)

b) \(x^2-25+y^2+2xy\)

c) \(x^2-xy+x-y\)

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

Answer 1

a)\(x^2-y^2-2x+2y\))

= (x - y)(x + y) - 2(x - y)

= (x - y)(x + y - 2)

b)\(x^2-25+y^2+2xy\)

= \(\left(x^2+2xy+y^2\right)\) \(-5^2\)

= \(\left(x+y\right)^2-5^2\)

= (x + y - 5)(x + y + 5)

c) \(x^2-xy+x-y\)

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

= x(x + 1) - y(x + 1)

= (x + 1)(x - y)

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

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

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

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

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

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

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