Question

разложите на множители: 49x²-4y²
x²-18x+81
y³-4y
x³-y³+x²y-xy
x¹⁸-4x⁹+4​

Answer 1

Ответ:

$49 {x}^{2} - 4 {y}^{2} = (7x - 2y)(7x + 2y)$

${x}^{2} - 18x + 81 = {(x - 9)}^{2}$

${y}^{3} - 4y = y( {y}^{2} - 4) = y(y - 2)(y + 2)$

${x}^{3} - {y}^{3} + {x}^{2} y - x {y}^{2} = (x - y)( {x}^{2} + xy + {y}^{2} ) + xy(x - y) = (x - y)( {x}^{2} + xy + {y}^{2} + xy) = (x - y)( {x}^{2} + 2xy + {y}^{2} ) = (x - y) {(x + y)}^{2}$

${x}^{18} - 4 {x}^{9} + 4 = {( {x}^{9} - 2) }^{2}$