Question

1. Разложите на множители многочлен: a) 25b² - x6: 6) 8x³ + 216​

Answer 1

а)

25b²-x⁶=(5b)²-(x³)²=(5b-x³)(5b+x³)

б)

8х³+216=(2х)³+6³=(2х+6)(4х²-12х+36)=

=2(х+3)4(х²-3х+9)=8(х+3)(х²-3х+9)

Answer 2

$\displaystyle\bf\\1)\\\\25b^{2} -x^{6} =(5b)^{2} -(x^{3} )^{2} =(5b-x^{3} )\cdot(5b+x^{3} )\\\\\\2)\\\\8x^{3} +216=8\cdot(x^{3} +27)=8\cdot(x^{3} +3^{3} )=8\cdot(x+3)\cdot(x^{2} -3x+9)$