\(2x^4-7x^3+17x^2-20x+14\)

\(=2x^4-3x^3+7x^2-4x^3+6x^2-14x+4x^2-6x+14\)

\(=x^2\left(2x^2-3x+7\right)-2x\left(2x^2-3x+7\right)+2\left(2x^2-3x+7\right)\)

\(=\left(x^2-2x+2\right)\left(2x^2-3x+7\right)\)

\(4\left(x+2\right)\left(x+3\right)\)

4x² + 20x + 24 

= 4 ( x² + 5x + 6 ) = 4 ( x + 3 ) ( x + 2 )

a) ( x 2  – 4x + 1)( x 2  – 2x + 3).     b) (3x – y – 1)(x – 7y – 1).

\(15\left(x-y\right)-20x\left(y-x\right)=\left(15+20x\right)\left(x-y\right)=5\left(3+4x\right)\left(x-y\right)\)

\(15\left(x-y\right)-20x\left(y-x\right)\)

\(=15\left(x-y\right)+20x\left(x-y\right)\)

\(=5\left(x-y\right)\left(3+4x\right)\)

\(=4xy\left(1-5x^2y+4xy\right)\)

=4xy(1-  5x²y+4xy) 

= 4xy ( 1 - 20x²y + 4xy )

\(x^4+x^3-20x^2-47x-15\)

\(=x^3\left(x-5\right)+6x^2\left(x-5\right)+10x\left(x-5\right)+3\left(x-5\right)\)

\(=\left(x-5\right)\left(x^3+6x^2+10x+3\right)\)

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

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

\(=x^4-5x^3+6x^3-30x^2+10x^2-50x+3x-15\\ =\left(x-5\right)\left(x^3+6x^2+10x+3\right)\\ =\left(x-5\right)\left(x^3+3x^2+3x^2+9x+x+3\right)\\ =\left(x-5\right)\left(x+3\right)\left(x^2+3x+1\right)\)

\(5\left(x^2+y^2\right)^2-20x^2y^2\)

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

\(=5\left(x^2-y^2\right)^2\)

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

Lời giải:

$5(x^2+-y^2)^2-20x^2y^2=5(x^2-y^2)^2-20x^2y^2$

$=5[(x^2-y^2)^2-(2xy)^2]=5(x^2-y^2-2xy)(x^2-y^2+2xy)$