Question

В) 4x(x-1)-2(2(x^2)-1)= г) 5a ((a^2)-3a)-3(a(a^2)-5a)= д)7b(4c-b)+4c(c-7b)= е)-2y((x^3)-2)-3((x^3)y+4y)= ж)3(m^2)(m+5n)-2n(8(m^2)-n)= з) 6(m^2)()(6(m^2)n+n-1) 50 б

Answer 1

$1)\quad 4x(x-1)-2(2x^2-1)=4x^2-4x-4x^2+2=\\\\=-4x+2=-2(2x-1)\\\\2)\quad 5a(a^2-3a)-3(aa^2-5a)=5a^3-15a^2-3a^3+15a=\\\\=2a^3-15a^2+15a=a(2a^2-15a+15)=\\\\=a(a-\frac{15-\sqrt{105}}{4})(a-\frac{15+\sqrt{105}}{4})\\\\3)\quad 7b(4c-b)+4c(c-7b)=28bc-7b^2+4c^2-28bc=\\\\=4c^2-7b^2=(2c-\sqrt7c)(2b+\sqrt7b)\\\\4)\quad -2y(x^3-2)-3(x^3y+4y)=-2x^3y+4y-3x^3y-12y=\\\\=-5x^3y-8y=-y(5x^3+8)=-y(\sqrt[3]5x+2)(\sqrt[3]{25}x^2-2\sqrt[3]5x+4)$

$5)\quad 3m^2(m+5n)-2n(8m^2-n)=\\\\=3m^3+15m^2n-16m^2n+2n^2=3m^3-m^2n+2n^2=\\\\=m^2(3m-n)+2n^2\\\\6)\quad 6m^2n^3-n^2(6m^2n+n-1)==\\\\=6m^2n^3-6m^2n^3-n^2(n-1)=-n^2(n-1)=n^2(1-n)$