Question

Срочно! Даю 60 баллов РОВНО! Разложите на множители: 1)81c^2-d^2+9c+d 2)a^2+8ab+16b^2-1 3)ax^6-3x^6-ax^3+3x^3 4)25-m^2-12mn-36n^2

Answer 1

1)(9с+d)(9c-d+1)
2)(a+4b-1)(a+4b+1)
3)x^3(a-3)(x-1)(x^2+x+1)
4)(5-m-6n)(5+m+6n)

Answer 2

1)81c^2-d^2+9c+d=(9c-d)(9c+d)+(9c+d)=(9c+d)(9c-d+1)

2)a^2+8ab+16b^2-1=(a+4b)^2-1^2=(a+4b-1)(a+4b+1)

3)
ax^6-3x^6-ax^3+3x^3=x^3(ax^3-3x^3-a+3)=x^3(x^3(a-3)-(a-3))=
=x^3(a-3)(x^3-1)=(x^3(a-3)(x-1)(x^2+x+1)

4)25-m^2-12mn-36n^2=25-(m+6n)^2=(5+m+6n)(5-m-6n)