Lời giải:

a.

$=(x^2)^2+(\frac{1}{2}y^4)^2+2.x^2.\frac{1}{2}y^4-x^2y^4$

$=(x^2+\frac{1}{2}y^4)^2-(xy^2)^2$
$=(x^2+\frac{1}{2}y^4-xy^2)(x^2+\frac{1}{2}y^4+xy^2)$
b.

$=(\frac{1}{2}x^2)^2+(y^4)^2+2.\frac{1}{2}x^2.y^4-x^2y^4$
$=(\frac{1}{2}x^2+y^4)^2-(xy^2)^2$
$=(\frac{1}{2}x^2+y^4-xy^2)(\frac{1}{2}x^2+y^4+xy^2)$

c.

$=(8x^2)^2+(y^2)^2+2.8x^2.y^2-16x^2y^2$

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

d.

$=\frac{64x^4+y^4}{64}=\frac{1}{64}(8x^2+y^2-4xy)(8x^2+y^2+4xy)$

c: \(64x^4+y^4\)

\(=64x^4+16x^2y^2+y^4-16x^2y^2\)

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

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

a. = \(\left(x^3+x^2\right)+\left(7x^2+7x\right)+\left(10x+10\right)\)

= \(x^2\left(x+1\right)+7x\left(x+1\right)+10x\left(x+1\right)\)

= \(\left(x+1\right)\left(x^2+7x+10x\right)\)

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

x⁴ + x²y² +y⁴                   

= (x²)² +  x²y² + (y²)²          

= (x²)² +  x²y² + (y²)²  + x²y² - x²y²       

= (x²)² +  2 x²y² + (y²)²  - x²y²      

= (x² + y²)²- (xy)²                  

=(x² + y² + xy)(x² + y² - xy)

Ta có:

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

b) \(\left(a^2+b^2\right)^2-4a^2b^2\)

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

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

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

\(x^4-y^4+2x^3y-2xy^3\)

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

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

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

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

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

a) \(6x^2-11x+3\)

\(=6x^2-9x-2x+3\)

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

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

b) \(2x^2+3x-27\)

\(=2x^2-6x+9x-27\)

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

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

Lời giải:

a. $A=9x^2+15x+6xy+y^2+5y=(9x^2+6xy+y^2)+(15x+5y)$
$=(3x+y)^2+5(3x+y)=0^2+5.0=0$

b. $25x^2-y^4-5x+y^2=(25x^2-y^4)-(5x-y^2)=(5x-y^2)(5x+y^2)-(5x-y^2)$

$=(5x-y^2)(5x+y^2-1)$

`x^4+x^2 y^2+y^4`

`=x^4+2x^2 y^2 +y^4-x^2 y^2`

`=(x^2+y^2)^2-(xy)^2`

`=(x^2-xy+y^2)(x^2+xy+y^2)`