Question

Разложите на множители: 14-14m² 3a-3a³ 7x^5-7xy² 5x²y²-45a²b² 3x²-24xy+48y² -3a^4-12a³-12a² 2a³+54b^6 x³-yx-x²+yx² a+5b+a²-25b² ac^6-ac^4-c^6+c^4

Answer 1

$\sf 14-14m^2=14(1-m^2)=14(1-m)(1+m)\\ 3a-3a^3=3a(1-a^2)=3a(1-a)(1+a)\\ 7x^5-7xy^2=7x(x^4-y^2)=7x(x^2-y)(x^2+y)\\ 5x^2y^2-45a^2b^2=5(x^2y^2-9a^2b^2)=5(xy-3ab)(xy+3ab)\\ 3x^2-24xy+48y^2=3(x^2-8xy+16y^2)=3(x-4y)^2\\ -3a^4-12a^3-12a^2=-3a^2(a^2+4a+4)=-3a^2(a+2)^2\\ 2a^3+54b^6=2(a^3+27b^6)=2(a+3b^2)(a^2-3ab^2+9b^4)\\ x^3-yx-x^2+yx^2=x^2(x-1)+yx(x-1)=(x-1)(x^2+yx)=x(x-1)(x+y)$

$\sf a+5b+a^2-25b^2=a+5b+(a-5b)(a+5b)=(a+5b)(a-5b+1)\\ ac^6-ac^4-c^6+c^4=c^6(a-1)-c^4(a-1)=(a-1)(c^6-c^4)=\\ =c^4(a-1)(c^2-1)=c^4(a-1)(c-1)(c+1).$