Question

Разложите на множители:
а) 4xy + 12y - 4x -12;

б) 60 + 6ab - 30b -12a;

в) -abc -5ac - 4ab -20a;

г) a³ + a²b + a² + ab.

Answer 1

$4xy+12y-4x-12=(4xy-4x)+(12y-12)=4x(y-1)+12(y-1)$$=(4x+12)(y-1)$$=4(x+3)(y-1)$

$60+6ab-30b-12a=(60-30b)+(6ab-12a)=$$30(2-b)+6a(b-2)=30(2-b)-6a(2-b)=(2-b)(30-6a)$=$=6(2-b)(5-a)$

$-abc-5ac-4ab-20a=(-abc-5ac)-(4ab+20a)=$$-ac(b+5)-4a(b+5)=(b+5)(-ac-4a)$$=-a(b+5)(c+4)$

$a^3+a^2b+a^2+ab=a^2(a+b)+a(a+b)=(a+b)(a^2+a)=a(a+b)$$(a+1)$