Question

Phân tích đa thức thành nhân tử:

a) \(\left(x-z\right)^2-y^2+2y-1\)

b) \(x^3+y^3+3y^2+3y+1\)

c) \(1-2a+2bc+a^2-b^2-c^2\)

d) \(x^2+3cd\left(2-3cd\right)-10xy-1+25y^2\)

e) \(bc\left(b+c\right)+ac\left(c-a\right)-ab\left(a+b\right)\)

Answer 1

a, \(\left(x-z\right)^2-y^2+2y-1\)

\(=\left(x-z\right)^2-\left(y-1\right)^2\)

\(=\left(x-z-y+1\right)\left(x-z+y-1\right)\)

b, \(x^3+y^3+3y^2+3y+1\)

\(=x^3+\left(y+1\right)^3=\left(x+y+1\right)\left[x^2-x\left(y+1\right)+\left(y+1\right)^2\right]\)

\(=\left(x+y+1\right)\left(x^2-xy-x+y^2+2y+1\right)\)

c, \(1-2a+2bc+a^2-b^2-c^2\)

\(=a^2-2a+1-\left(b^2-2bc+c^2\right)\)

\(=\left(a-1\right)^2-\left(b-c\right)^2\)

\(=\left(a-1-b+c\right)\left(a-1+b-c\right)\)

d, \(x^2+3cd\left(2-3cd\right)-10xy-1+25y^2\)

\(=\left(x^2-10xy+25y^2\right)+\left[3cd\left(2-3cd\right)-1\right]\)

\(=\left(x-5y\right)^2+\left(6cd-\left(3cd\right)^2-1\right)\)

\(=\left(x-5y\right)^2-\left(3cd-1\right)^2\)

\(=\left(x-5y-3cd+1\right)\left(x-5y+3cd-1\right)\)

Chúc bạn học tốt!!!

Answer 2

Giúp bạn câu e nè
e) bc ( b + c) + ac ( c - a) - ab ( a + b)
= b² c + bc² + ac ² - a²c - a²b - ab²
= ( b² c - a²c ) + ( bc²+ ac² ) - ( a²b + ab² )
= c ( b²- a² ) + c² ( b+ a ) - ab(a + b)
= c( b - a )( b + a) + c² ( b+ a ) - ab(a + b)
= ( b+ a )( bc - ac + c²- ab )
= ( b+ a )( ( bc - ab ) - ( ac - c² ))
= ( b+ a )( b( c - a ) - c ( a - c))
= ( b+ a )( b( c - a ) + c ( c - a))
= ( b+ a )( c - a )(b + c )