Mnohočleny a lomené výrazy

9000101707

Časť: 
C
Upravte na súčin. \[ x^{6} - 1 \]
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + x + 1\right )\left (x^{2} - x + 1\right )\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + x + 1\right )\left (x^{2} - x - 1\right )\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + 2x + 1\right )\left (x^{2} - 2x + 1\right )\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + x - 1\right )\left (x^{2} - x + 1\right )\)

9000101605

Časť: 
B
Umocnite daný výraz \(\left (4x^{2}y + 2xy^{2}\right )^{3}\).
\(64x^{6}y^{3} + 96x^{5}y^{4} + 48x^{4}y^{5} + 8x^{3}y^{6}\)
\(16x^{2}y^{3} + 24x^{3}y^{3} + 8x^{3}y^{6}\)
\(64x^{6}y^{3} + 96x^{3}y^{3} + 96x^{4}y^{5} + 8x^{3}y^{6}\)
\(64x^{6}y^{3} + 8x^{3}y^{6}\)

9000101710

Časť: 
B
Upravte na súčin. \[ x^{2}y - x^{2}z - 4xyz + 4xy^{2} + 4y^{3} - 4y^{2}z \]
\(\left (y - z\right )\left (x + 2y\right )^{2}\)
\(\left (y - z\right )\left (x - 2y\right )^{2}\)
\(\left (y - z\right )\left (x^{2} + 4y + 4y^{2}\right )\)
\(\left (y + z\right )\left (x - 2y\right )^{2}\)

9000101704

Časť: 
B
Upravte na súčin. \[ 16x^{2}y^{4} - 25x^{4}y^{2} \]
\(\left (4xy^{2} - 5x^{2}y\right )\left (4xy^{2} + 5x^{2}y\right )\)
\(\left (4xy - 5x^{2}y\right )\left (4xy^{2} + 5xy\right )\)
\(\left (4x^{2}y^{2} - 5xy\right )\left (4x^{2}y^{2} + 5xy\right )\)
\(\left (4xy^{2} - 5x^{2}y\right )^{2}\)