Bài khó quá

4x⁴+4x-3= (2x)²+2(2x)+1-4

=(2x+1)²-2²=(2x+1-2)(2x+1+2)

=(2x-1)(2x+3)

bn làm đ rùi, tui đ cho bn

\(-4x^2+12xy-9y^2+25=25-\left(2x-3y\right)^2=\left(5-2x+3y\right)\left(5+2x-3y\right)\)

\(-4x^2+12xy-9y^2+25\)

\(=25-\left(4x^2-12xy+9y^2\right)\)

\(=25-\left(2x-3\right)^2\)

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

\(-4x^2+12xy-9y^2+25\)
\(=\left(-4x^2+12xy-9y^2\right)+25\)
\(=-\left(4x^2-12xy+9y^2\right)+25\)
\(=-\left(2x-3y\right)^2+25\)
Chúc học tốt tick mk nha

a)   x³ -2x² +5x-4

=x³-x²-x²+x+4x-4

=x²(x-1)-x(x-1)+4(x-1)

=(x²-x+4)(x-1)

b) x³-x²+x+3

=x³+x²-2x²-2x+3x+3

=x²(x+1) -2x(x+1)+3(x+1)

=(x²-2x+3)(x+1)

c) 6x³+x²+x+1

=6x³+ 3x²-2x²-x+2x+1

=6x²(x+\(\frac{1}{2}\)) - 2x(x+\(\frac{1}{2}\)) +2(x+\(\frac{1}{2}\))

=(6x²-2x+2) (x+\(\frac{1}{2}\))

=2( 3x²-x+1) (x+\(\frac{1}{2}\))

d)  4x³ + 6x²+4x+1

= 4x³+2x²+4x²+2x+2x+1

= 4x²(x+\(\frac{1}{2}\))+ 4x(x+\(\frac{1}{2}\))+2(x+\(\frac{1}{2}\))

= 2(2x² +2x+1)( x+\(\frac{1}{2}\))

e) x⁶ -9x³+8

\(12x-9-4x^2=-\left(2x-3\right)^2\\ Sửa:x^3-6x^2y+12xy^2-8y^3=\left(x-2y\right)^3\)

1, = 6(x^2 .y -z^2 +10x+25 )

2, = x^2 -2x-9x+18

    = x(x-2)-9(x-2)

    = (x-9)(x-2)

\(=-2x^2+6xy-3y^2+25\)

\(=-\left(2x^2-6xy+3y^2\right)+25\)

\(=-\left(2x^2+3y^2\right)+25\)

\(=\left(2x^2-3y^2\right)+25\)

\(=\left(2x^2+3y^2\right).\left(2x^2-3y^2\right)+25\)

quên rùi

\(-4x^2+12xy-9y^2+25=\left(-4x^2+6xy+10x\right)+\left(6xy-9y^2-15y\right)-\left(10x-15y-25\right)\)

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

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

1/(x+2)² -(3x-1)²=(x+2+3x-1)(x+2-3x+1)=4x(-2x+3)=-8x²+12x

2/(x⁴+x²)(-2x³-2x)=x²(x²+1)-2x(x²+1)=(x²+1)(x²-2x)

Bài 1:

\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)

Bài 3:

\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)

Bài 1;

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

2) \(6x^2+12xy+6y^2=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\)

3) \(2y^3+8y^3+8y=10y^3+8y=2y\left(5y^2+4\right)\)

4) \(5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

1) \(x^3-64x=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\)

2) \(8x^2y-18y=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\)

3) \(24x^3-3=3\left(8x^3-1\right)=3\left(2x-1\right)\left(4x^2+2x+1\right)\)

Bài 3:

1) \(5x^2+10x+5-5y^2=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y\right]=5\left(x-y+1\right)\left(x+y+1\right)\)

2) \(3x^3-6x^2+3x-12xy^2=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-\left(2y\right)^2\right]=3x\left(x-2y-1\right)\left(x+2y-1\right)\)

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

4) \(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2-4x+4y\right)=2x\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]=2x\left(x-y\right)\left(x+y-4\right)\)

= x^2(X-1) - 4(x^2-2x+1)

=x^2(x-1)-4(x-1)^2

=(x-1)(x^2-4x+4)

=(x-1)(x-2)^2