Lời giải:

a.

$64x^2-24y^2=8(8x^2-3y^2)=8(\sqrt{8}x-\sqrt{3}y)(\sqrt{8}x+\sqrt{3}y)$

b.

$64x^3-27y^3=(4x)^3-(3y)^3=(4x-3y)(16x^2+12xy+9y^2)$

c.

$x^4-2x^3+x^2=(x^2-x)^2=[x(x-1)]^2=x^2(x-1)^2$

d.

$(x-y)^3+8y^3=(x-y)^3+(2y)^3=(x-y+2y)[(x-y)^2-2y(x-y)+(2y)^2]$

$=(x+y)(x^2-4xy+7y^2)$

a) \(64x^2-24y^2\)

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

b) \(64x^3-27y^3\)

\(=\left(4x\right)^3-\left(3y\right)^3\)

\(=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)

c) \(x^4-2x^3+x^2\)

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

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

d) \(\left(x-y\right)^3+8y^3\)

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

\(=\left(x+y\right)\left(x^2-4xy+7y^2\right)\)

b: 6x^2-24y^2

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

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

c: =(4x)^3-(3y)^3

=(4x-3y)(16x^2+12xy+9y^2)

d: x^4-2x^3-x^2

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

a: \(x^4-2x^3+x^2-2x\)

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

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

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

b: \(x^4+x^3-8x-8\)

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

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

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

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

a) \(\left(x+1\right)\left(x+2\right)\left(x+4\right)\left(x+5\right)-4=\left(x^2+6x+5\right)\left(x^2+6x+8\right)-4\)

Đặt \(t=x^2+6x+5\)

\(PT=t\left(t+3\right)-4=t^2+3t-4=\left(t-1\right)\left(t+4\right)\)

Thay t: \(PT=\left(x^2+6x+5-1\right)\left(x^2+6x+5+4\right)=\left(x^2+6x+4\right)\left(x^2+6x+9\right)=\left(x^2+6x+4\right)\left(x+3\right)^2\)

b)  Đặt \(t=\left(2x+1\right)^2\)

\(PT=t^2-3t+2=\left(t^2-3t+\dfrac{9}{4}\right)-\dfrac{1}{4}=\left(t+\dfrac{3}{2}\right)^2-\dfrac{1}{4}=\left(t+1\right)\left(t+2\right)\)

Thay t:

\(PT=\left[\left(2x+1\right)^2+1\right]\left[\left(2x+1\right)^2+2\right]=\left[4x^2+4x+2\right]\left[4x^2+4x+3\right]=2\left[2x^2+2x+1\right]\left[4x^2+4x+3\right]\)

a) \(4x\left(a-b\right)+6xy\left(b-a\right)\)

\(=4x\left(a-b\right)-6xy\left(a-b\right)\)

\(=\left(4x-6xy\right)\left(a-b\right)\)

\(=2x\left(2-3y\right)\left(a-b\right)\)

b) \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)

\(=3\left(2x+1\right)-\left(2x-5\right)\left(2x+1\right)\)

\(=\left(3-2x+5\right)\left(2x+1\right)\)

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

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

g: \(\left(3x-1\right)^2-\left(x+3\right)^2\)

\(=\left(3x-1-x-3\right)\left(3x-1+x+3\right)\)

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

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

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

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

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

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

------------------------------------

\(a^3+3a^2-6a-8\)

\(=a^3+4a^2-a^2-4a-2a-8\)

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

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

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

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

\(=\left(a+4\right)\left[\left(a^2-2a\right)+\left(a-2\right)\right]\)

\(=\left(a+4\right)\left[a\left(a-2\right)+\left(a-2\right)\right]\)

\(=\left(a+4\right)\left(a-2\right)\left(a+1\right)\)

---------------------------------

\(2x^2-5x+2\)

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

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

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

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

-----------------------------------------

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

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

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

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

-------------------------------------

\(a^2-1+4b-4b^2\)

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

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

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

----------------------------------------

\(a^4+6a^2b+9b^2-1\)

\(=\left(a^4+6a^2b+9b^2\right)-1\)

\(=\left(a^2+3b\right)^2-1\)

\(=\left(a^2+3b-1\right)\left(a^2+3b+1\right)\)

---------------------------------

\(2x^3+16y^3\)

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

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

Lần sau ghi đề tách riêng từng câu ra nhé em. Ghi dính chùm vậy khó nhìn lắm. Sẽ ít ai giải cho em

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

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

3) \(xy\left(x+y\right)-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\) (xem lại đề sửa -2x thành -x mới đúng)

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