Odpowiedź:
a)
[tex]( { {2x}^{2} + {y}^{4} )}^{2} = {4x}^{4} + {4x}^{2} { y}^{4} + {y}^{8} [/tex]
b)
[tex](2 \frac{2}{3} - {x}^{2} )^{2} = ( \frac{8}{3} - {x}^{2} )^{2} = \frac{64}{9} - \frac{16}{3} {x}^{2} + {x}^{4} = 7 \frac{1}{9} - 5 \frac{1}{3} {x}^{2} + {x}^{4} [/tex]
c)
[tex]( {4x - y})^{3} = {64x}^{3} - {48x}^{2} y + 12x {y}^{2} - {y}^{3} [/tex]
d)
[tex]( {2 + 3 \sqrt{5} )}^{2} = 4 + 12 \sqrt{5} + 45 = 49 + 12 \sqrt{5} [/tex]
e)
[tex](4 - {2 \sqrt{2} })^{2} = 16 - 16 \sqrt{2 } + 8 = 24 - 16 \sqrt{2} [/tex]
f)
[tex](4 - \sqrt{3})(4 + \sqrt{3} ) = 16 - 3 = 13 [/tex]
Szczegółowe wyjaśnienie:
wzory skróconego mnożenia
[tex](x + {y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ \\ (x - y )^{2} = { x}^{2} - 2xy + {y}^{2} \\ \\ (x + y)(x - y) = {x }^{2} - y^{2} [/tex]
