Question

bài 1: nhân đơn thức với đa thức

a) (a+b+c).(a²+b²+c²-ab-bc-ca)        b) (a-b).(a+b)

c) (x-y).(x²+xy+y²)              d) \(\dfrac{2}{3}\)xy(x²yz+\(\dfrac{2}{5}\)x-\(\dfrac{7}{4}\)y)

e) (x³-3x²+3x-1).(x²-4+3x)

 

Answer 1

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

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

d: \(=\dfrac{2}{3}x^3y^2z+\dfrac{4}{15}x^2y-\dfrac{7}{6}xy^2\)

 

Answer 2

a) (a+b+c).(a²+b²+c²-ab-bc-ca)

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

=\(a^3+b^3+c^3-3abc\)

 b) (a-b).(a+b)

=\(\left(a^2-b^2\right)\)

c) (x-y).(x²+xy+y²)

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

=\(x^3-y^3\)

 d) \(\dfrac{2}{3}\)xy(\(x^2yz+\dfrac{2}{5}x-\dfrac{7}{4}y\))

=\(\dfrac{2}{3}x^3y^2z+\dfrac{4}{15}x^2y-\dfrac{14}{12}xy^2\)

=\(\dfrac{2}{3}x^3y^2z+\dfrac{4}{15}x^2y-\dfrac{7}{6}xy^2\)

e) (x³-3x²+3x-1).(x²-4+3x)

=\(x^5-3x^4+3x^3-x^2-4x^3+12x^2-12x+4+3x^4-9x^3+9x^2-3x\)

=\(x^5-10x^3+20x^2-15x+4\)