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

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

\(=\left[a^2-\left(b^2-2bc+c^2\right)\right].\left[\left(b^2+2bc+c^2\right)-a^2\right]\)

\(=\left[a^2-\left(b-c\right)^2\right].\left[\left(b+c\right)^2-a^2\right]\)

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

\(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)

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

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

Tham khảo nhé~

a: =64x^4+16x^2y^2+y^4-16x^2y^2

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

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

b: =x^8+2x^4+1-x^4

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

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

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

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

c: =(x+1)(x^2-x+1)+2x(x+1)

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

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

d: =(x^2-1)(x^2+1)-2x(x^2-1)

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

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

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

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

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

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

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

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

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

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

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

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

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) \(\left(x-y\right)^3+8y^3\)

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

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

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

b) \(\left(x+2\right)^2-9=\left(x-1\right)\left(x+5\right)\)

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

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

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

`a, 4x^2-1 = (2x+1)(2x-1)`

`b, (x+2)^2-9 = (x+2-3)(x+2+3) = (x-1)(x+5)`

`c, (a+b)^2-(a-2b)^2 = (a+b+a-2b)(a+b-a+2b) = (2a-b)(3b)`

Khó quá , bó tay 

\(\left(x^2-2x+2\right)^4-20x^2\left(x^2-2x+2\right)+64x^4\)

\(=\left[\left(x^2-2x+2\right)^2\right]^2-2.\left(x^2-2x+2\right)^2.10x^2+\left(10x^2\right)^2-36x^4\)

\(=\left[\left(x^2-2x+2\right)^2-10x^2\right]^2-\left(6x^2\right)^2\)\(=\left[\left(x^2-2x+2\right)^2-4x^2\right]\left[\left(x^2-2x+2\right)^2-16x^2\right]\)

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

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