Question

Разложите на множители: 1)81c²-d²+9c+d; 2)a²+8ab+16²-1; 3)ax(6маленькая)-3x(6маленькая)-ax³+3x³; 4)25-m²-12mn-36n²:

Answer 1

1)81c²-d²+9c+d=(9с)²-d²+9c+d=(9c-d)(9c+d)+(9c+d)=(9c+d)(9c-d+1);
2)a²+8ab+16-1=a²+2*4ab+4²-1=(а + 4b)²-1 =(а + 4b - 1)(а + 4b+1);
3)ax⁶-3x⁶-ax³+3x³=x³(ax³-3x³-a+3)=x³(x³(a-3)-(a-3))=x³(x³-1)(a-3);
4)25-m²-12mn-36n²=25-(36n²+12mn+m²)= 5²-(6n+m)²=(5-6n-m)(5+6n+m).