b, \(a+b+2\sqrt{a.b}=\sqrt{a^2}+\sqrt{b^2}+2\sqrt{ab}=\left(\sqrt{a}+\sqrt{b}\right)^2\) ( Vì a, b >= 0 )

c, \(a+b-2\sqrt{a.b}=\sqrt{a^2}+\sqrt{b^2}-2\sqrt{ab}=\left(\sqrt{a}-\sqrt{b}\right)^2\)( Vì a, b >= 0 )

a) \(4a^3b^3c^2x+12a^3b^4c^2-16a^4b^5cx\)

\(=4a^3b^3c\left(cx+3bc-4ab^2x\right)\)

b) \(\left(b-2c\right)\left(a-b\right)-\left(a+b\right)\left(2c-b\right)\)

\(=\left(b-2c\right)\left(a-b+a+b\right)=2a\left(b-2c\right)\)

c) \(3a\left(a+5\right)-2\left(5+a\right)=\left(a+5\right)\left(3a-2\right)\)

d) \(\left(x+1\right)^2-3\left(x+1\right)=\left(x+1\right)\left(x+1-3\right)\)

\(\left(a^2+b^2+c^2\right)^2-a^2b^2-b^2c^2-a^2c^2\)

\(=a^4+b^4+a^2b^2+2a^2b^2+2a^3b+2ab^3-a^2b^2-b^2c^2-c^2a^2\)

\(=\left(a^4+2a^2b^2+b^4\right)+\left(2a^3b+2ab^3\right)-\left(a^2c^2+b^2c^2\right)\)

\(=\left(a^2+b^2\right)^2+2ab.\left(a^2+b^2\right)-c^2.\left(a^2+b^2\right)\)

\(=\left(a^2+b^2\right).\left(a^2+b^2+2ab-c^2\right)\)

\(=\left(a^2+b^2\right).\left[\left(a+b\right)^2-c^2\right]\)

\(=\left(a^2+b^2\right).\left(a+b-c\right).\left(a+b+c\right)\)

a) \(5a^2-5ax-7a+7x\)

\(=5a\left(a-x\right)-7\left(a-x\right)\)

\(=\left(5a-7\right)\left(a-x\right)\)

c) \(x^2-\left(a+b\right).x+ab\)

\(=x^2-ax-bx+ab\)

\(=x\left(x-a\right)-b\left(x-a\right)\)

\(=\left(x-b\right)\left(x-a\right)\)

a,\(5a^2-5ax-7a+7x=5a\left(a+x\right)-7\left(a+x\right)=\left(a+x\right)\left(5a-7\right)\)

a: =x^2+2xy+y^2-4x^2y^2

=(x+y)^2-(2xy)^2

=(x+y+2xy)(x+y-2xy)

b: =49-(a^2-2ab+b^2)

=49-(a-b)^2

=(7-a+b)(7+a-b)

c: =\(a^2-\left(b^2-4bc+4c^2\right)\)

\(=a^2-\left(b-2c\right)^2=\left(a-b+2c\right)\left(a+b-2c\right)\)

d: 

\(=\left(bc\right)^2-\left(b^2+c^2-a^2\right)^2\)

\(=\left(bc-b^2-c^2+a^2\right)\left(bc+b^2+c^2-a^2\right)\)

e: \(=\left(a+b\right)^2+2c\left(a+b\right)+c^2+\left(a+b\right)^2-2c\left(a+b\right)+c^2-4c^2\)

=2(a+b)^2-2c^2

=2[(a+b)^2-c^2]

=2(a+b-c)(a+b+c)

1.=[(1/2)a^2)^2-2.(1/2)a^2b+b^2
=[(1/2)a^2-b]^2
2.=2a^2+2b^2-2-a^2c+c-b^2c
=2(a^2+b^2-a)-c(a^2+b^2-1)
=(2-c)(a^2+b^2-1)