Question

Разложите на множители: 64х²-16ху+у² выполните действия: а) (с²-8в)(8в+с²); б) (4у²-у)² ; в) (3+п)²(3-п)²

Answer 1

$1)64 x^{2} -16xy+y ^{2} =(8x) ^{2} -2*8x*y+y ^{2} =(8x-y)^{2} \\ \\ 1)(c ^{2} -8b)(8b+c ^{2} )=(c ^{2} -8b)(c ^{2} +8b)=c ^{4} -64b ^{2} \\ \\ 2)(4y ^{2} -y) ^{2} =16y ^{4} +y ^{2} -8y ^{3} \\ \\ 3)(3+p) ^{2} *(3-p) ^{2} =(9+p ^{2} +6p)(9+p ^{2} -6p)= \\ =81+9p ^{2} -54p+9p ^{2} +p ^{4} -6p ^{3} +54p+6p ^{3} -36p ^{2} = \\ = 81+9p ^{2} +9p ^{2} +p ^{4} -36p ^{2} =p ^{4} -18p ^{2} +81$