Question

Разложить на множители
1)28-7$y^{2}$
2)-11$x^{2}$+22$x$-11
3)$x^{3} y$+8$y$
4)$(y^{2} - 1)^{2}-9$

Answer 1

28-7у²=7(4-у²)=7(2-у)(2+у)
-11х²+22х - 11= - 1(х²-2х+1)= - 11(х-1)(х-1= -11(х-1)²
х³у+8у=у(х³+8)=у(х+2)(х²-2х+4)
(у²-1)²-9=(у²-1)² - 3²=(у²-1-3)(у²-1+3)=(у²-4)(у²+2)=(у-2)(у+2)(у²+2)

Answer 2

1) 28 - 7y² = 7(4 - y²) = 7(2 - y)(2 + y)

2) - 11x² + 22x - 11 = -11(x² - 2x + 1) = -11(x - 1)² = -11(x - 1)(x - 1)

3) x³y + 8y = y(x³ + 8) = y(x³ + 2³) = y(x + 2)(x² - 2x + 4)

4) (y² - 1)² - 9 = (y² - 1)² - 3² = (y² - 1 - 3)(y² - 1 + 3) = (y² - 4)(y² + 2) =
= (y - 2)(y + 2)(y² + 2)