Lời giải:

$A=x^2-8xy+15y^2=x^2-3xy-(5xy-15y^2)$

$=x(x-3y)-5y(x-3y)=(x-3y)(x-5y)$

$B=2x^2-5xy+2y^2=(2x^2-4xy)-(xy-2y^2)$

$=2x(x-2y)-y(x-2y)=(2x-y)(x-2y)$

$C=2x^2-3y^2-xy=(2x^2+2xy)-(3y^2+3xy)$

$=2x(x+y)-3y(y+x)=(x+y)(2x-3y)$

khó quá mk nản chí rùi huhu!!

3463465655775676876897756232544545465657578768

b,tách x=-2x+x

a) 5x^2 + 6xy + y^2

=5x²+5xy+xy+y²

=5x.(x+y)+y.(x+y)

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

b) x^2 + 2xy - 15y^2.

=x²-3xy+5xy-15y²

=x.(x-3y)+5y.(x-3y)

=(x-3y)(x+5y)

c) (x-y)^2 + 4(x-y) - 12

=(x-y)²+4(x-y)+4-16

=(x-y+2)²-16

=(x-y+2-4)(x-y+2+4)

=(x-y-2)(x-y+6)

d) x^3 - 2x - 4.

=x³+2x²+2x-2x²-4x-4

=x.(x²+2x+2)-2.(x²+2x+2)

=(x²+2x+2)(x-2)

#)Giải :

\(x^3-2x-4\)

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

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

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

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

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

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

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

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

\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)

Câu 1.

Đoán được nghiệm là 2.Ta giải như sau:

\(x^3-2x-4\)

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

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

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

cảm ơn nha!

\(x^4+2x^2-24\)

\(=x^4-4x^2+6x^2-24\)

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

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

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

\(2x^4+128y^4\)

\(=2x^4+2.\left(8y^2\right)^2\)

\(=2\left[x^4+\left(8y^2\right)^2\right]\)

\(=2\left[x^4+2x^28y^2+\left(8y^2\right)^2-2x^28y^2\right]\)

\(=2\left[\left(x^2+8y^2\right)^2-\left(4xy\right)^2\right]\)

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

2x4+128x^4

2x^4+2.(8y^2)^2

2.(x^4+(8y^2)^2)

2.((x^2)^2+2.x^2.8y^2+(8y^2)^2-2x^2.8y^2)

2.(x^2+8y^2)-(4.x.y)^2

2.((x^2+8y^2)-4xy).((x^2+8y^2)+4xy)

2.(x^2+8y^2-4xy).(x^2+8y^2+4xy)

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

x³-3x²-4=