Question

Phân tích đa thức sau thành nhân tử:

a, x^3-x^2y-25x+25y

b, b^2-4b+4a-a^2

c, x^3-4x^2-8x+8

d, x^2(x-1)-4x^2+8x-4

e, x^2-9xy+20y^2

f, x^2-x-12

Answer 1

Phân tích các đa thức sau thành nhân tử ... c) 6x(x+y)^2+3x^2y(x+y). 2: .... x³ - 5x + 8x - 4=x² . x -5x + 8x -2² = (x² - 2²) . (x -5x + 8x )=(x-2) . (x+2) . 4x. x³ - 9x² ..... Phân tích các đa thức sau thành nhân tử : a,x^3+5x^2+8x+4 b, x^3-9x^2+6x+16 .

Answer 2

\(a.=x^2\left(x-y\right)-25\left(x-y\right)\)

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

\(b.=\left(b-a\right)\left(b+a\right)-4\left(b-a\right)\)

\(=\left(b+a-4\right)\left(b-a\right)\)

Answer 3

a ) x³ - x²y - 25x + 25y

= x² . ( x - y ) - 25 . ( x - y )

= ( x - y )( x² - 25 )

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

b ) b² - 4b + 4a - a²

= ( b² - a² ) - ( 4b - 4a )

= ( b - a )( a + b ) - 4 . ( b - a )

= ( b - a )( a + b - 4 )

c ) x³ - 4x² - 8x + 8

= ( x³ + 8 ) - ( 4x² + 8x )

= ( x + 2 )( x² - 2x + 4 ) - 4x . ( x + 2 )

= ( x + 2 )( x² - 2x + 4 - 4x )

= ( x + 2 )( x² - 6x + 4 )

Answer 4

a) \(x^3-x^2y-25x+25y\)

\(=x^2\left(x-y\right)-25\left(x-y\right)\)

\(=\left(x-y\right)\left(x^2-25\right)\)

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

b) \(b^2-4b+4a-a^2\)

\(=\left(b^2-a^2\right)-\left(4b-4a\right)\)

\(=\left(b-a\right)\left(b+a\right)-4\left(b-a\right)\)

\(=\left(b-a\right)\left(b+a+4\right)\)

c) \(x^3-4x^2-8x+8\)

\(=\left(x^3+8\right)-\left(4x^2+8x\right)\)

\(=\left(x+2\right)\left(x^2-2x+4\right)-4x\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-2x+4-4x\right)\)

\(=\left(x+2\right)\left(x^2-6x+4\right)\)

\(=\left(x+2\right)\left(x^2-2.x.3+9-9+4\right)\)

\(=\left(x+2\right)\left[\left(x-3\right)^2-5\right]\)

\(=\left(x+2\right)\left(x-3-\sqrt{5}\right)\left(x-3+\sqrt{5}\right)\)

d) \(x^2\left(x-1\right)-4x^2+8x-4\)

\(=x^3-5x^2+8x-4\)

\(=\left(x^3-4x^2+4x\right)-\left(x^2-4x+4\right)\)

\(=x\left(x^2-4x+4\right)-\left(x^2-4x+4\right)\)

\(=\left(x^2-4x+4\right)\left(x-1\right)\)

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

e) \(x^2-9xy+20y^2\)

ko phân tích được vì lớn hơn 0

f) \(x^2-x-12\)

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

\(=x\left(x-4\right)+3\left(x-4\right)\)

\(=\left(x-4\right)\left(x+3\right)\)

Answer 5

a.=x^2 (x-y) -25(x-y)

=(x-y)(x^2-25)=(x-y)(x+5)(x-5)

b)=b^2 -4b+4a-a^2

=(b-a)(b+a) -4(b-a)

=(b-a)(b+a-4)

c)x^3-4x^2-8x+8

=(x^3+2x^2)-(6x^2+12x)+(4x+8)

=x^2(x+2)-6x(x+2)-4(x+2)

=(x+2)(x^2-6x-4)

=(x+2)[(x^2-6x+9)-13]

=(x+2)[(x-3)^2 -(căn 13)^2]

=(x+2)(x-3+căn 13)(x-3-căn 13)

Answer 6

Hoàng Nguyễn Văn

phần c làm theo bạn này nhé bài mình sai

Answer 7

Lê Tài Bảo Châu

câu e làm được nha

e) x^2-9xy+20y^2

=(x^2-4xy)-(5xy-20y^2)

=x(x-4y) - 5y(x-4y)

=(x-5y)(x-4y)

Answer 8

Hoàng Nguyễn Văn

ok thanks