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7m - 7 = 7(m - 1) = 7(m - 1)(m + 1)
x - x= x(x - 1) = x (x - 1)(x + 1)
5a - 5 = 5(a - 1) = 5(a - 1)(a + 1)
ab - ab = ab(a - b) = ab(a - b)(a + b)
5a - 20x = 5 (a - 4x) = 5(a - 2x)(a + 2x)
5m - 5mn = 5m(m - n) = 5m(m - n)(m + n)
7xy - 63xz = 7x(y - 9z) = 7x(y - 3z)(y + 3z)
pq - pq = pq(p - q) = pq(p - q)(p + q)
2x + 4xy + 2y = 2(x + 2xy + y ) = 2(x + y) = 2(x + y)(x + y)
5a + 10ab + 5b = 5(a + 2ab + b) = 5(a + b) = 5(a + b)(a + b)
3m - 6m + 3 = 3(m - 2m + 1) = 3 (m - 1) = 3(m - 1)(m - 1)
6p - 12p + 6 = 6(p + 2p + 1) = 6(p - 1) = 6(p - 1)(p - 1)
3xy + 6xy + 3x = 3x(y + 2y + 1) = 3x(y + 1) = 3x(y + 1)(y + 1)
2a - 4ab + 2ab = 2a(1 - 2ab + b) = 2a(1 - b) = 2a(1 - b)(1 - b)
12x + 24xy + 12xy = 12x(x + 2xy + y) = 12x(x + y) = 12x(x + y)(x + y)
9ab - 18ab + 9ab = 9ab(a - 2ab + b) = 9ab(a - b) = 9ab(a-b)(a-b)
(a + 1) - 4a = (a + 1 - 2a)(a + 1 + 2a) = (a - 1)(a + 1) =
= (a - 1)(a - 1)(a + 1)(a + 1)
(x + 4y) - 16xy = (x + 4y - 4xy)(x + 4y + 4xy) = (x - 2y)(x + 2y) =
= (x - 2y)(x - 2y)(x + 2y)(x + 2y)
36a - (a + 9) = (6a - a - 9)(6a+ a + 9) = -(a - 6a + 9)(a + 6a + 9) =
= - (a - 3)(a + 3) = - (a - 3)(a - 3)(a + 3)(a + 3)
81 - (x + 6x) = (9 - x - 6x)(9 + x + 6x) = -(x + 6x - 9)(x + 6x + 9)=
= - (x + 6x - 9)(x + 3) = -(x + 6x - 9)(x + 3)(x + 3)
 

1)7m^2-7=7(m^2-1)=7(m-1)(m+1)
2)x^3-x=x(x^2-1)=x(x-1)(x+1)
3)5a^2-5=5(а^2-1)=5(а-1)(а+1)
4)a^3b-ab^3=ab(a^2-b^2)=
=ab(a-b)(a+b)
5)5a^2-20x^2=5(a^2-4x^2)=
=5(a-2x)(a+2x)
6)5m^3-5mn^2=5m(m^2-n^2)=
=5m(m-n)(m+n)
7)7x^2y^2-63x^2z^2=7x^2(y^2-9z^2)=7x^2(y-3z)(y+3z)
8)p^4q^2-p^2q^4=p^2q^2(p^2-q^2)=p^2q^2(p-q)(p+q)
9)2x^2+4хy+2y^2=2(x^2+2xy+y^2)=2(x+y)^2
10)5a^2+10ab+5b^2=5(a^2+2ab+b^2)=5(a+b)^2
11)3m^2-6m+3=3(m^2-2m+1)=
=3(m-1)^2
12)6p^2-12p+6=6(p^2-2p+1)=
=6(p-1)^2
13)3xy^2+6ху+3х=3х(у^2+2у+1)=3х(у+1)^2
14)2a-4ab+2ab^2=2a(1-2b+
+b^2)=2a(b-1)^2
15)12х^5+24х^4у+12х^3у^2=
=12х^3(x^2+2xy+у^2)=
=12х^3(х+у)^2
16)9a^4b^2--18a^3b^3+9а^2b^4=
=9a^2b^2(a^2-2аb+b^2)=
=9a^2b^2(a+b)^2
17)(a^2+1)^2-4a^2=
=(a^2+1-2a)(a^2+1+2a)=
(a-1)^2(a+1)^2
18)(х^2+4у^2)^2-16x^2y^2=
=(x^2+4y^2-4xy)(x^2+4y^2+4xy)=(x+2y)^2
(x-2y)^2
19)36a^2-(a^2+9)^2=
=(6a-a^2-9)(6a+a^2+9)=
=-(a-3)^2(a+3)^2
20)81-(x^2+6x)^2=
=81-х^2(х+6)^2=(9-х)(х+9)(х+6)^2