Lời giải:
a. $x^2+2xy+y^2-81=(x+y)^2-9^2$
$=(x+y-9)(x+y+9)$
b. $4x^2-4x+1-36y^2$
$=(2x-1)^2-(6y)^2=(2x-1-6y)(2x-1+6y)$
c.
\(4y^2-(25-10x+x^2)=(2y)^2-(x-5)^2\)
$=(2y-x+5)(2y+x-5)$
d.
\(a^2-9+6x-x^2=a^2-(x^2-6x+9)=a^2-(x-3)^2\)
$=(a-x+3)(a+x-3)$
e.
$(x^2+4x+4)-(a^2-2ab+b^2)=(x+2)^2-(a-b)^2$
$=(x+2-a+b)(x+2+a-b)$
f.
$x^2-2xy+y^2-z^2+2zt-t^2$
$=(x^2-2xy+y^2)-(z^2-2zt+t^2)$
$=(x-y)^2-(z-t)^2=(x-y-z+t)(x-y+z-t)$
a: Ta có: \(x^2+2xy+y^2-81\)
\(=\left(x+y\right)^2-81\)
\(=\left(x+y+9\right)\left(x+y-9\right)\)
b: Ta có: \(4x^2-4x+1-36y^2\)
\(=\left(2x-1\right)^2-36y^2\)
\(=\left(2x-1-6y\right)\left(2x-1+6y\right)\)
c: Ta có: \(4y^2-\left(x^2-10x+25\right)\)
\(=4y^2-\left(x-5\right)^2\)
\(=\left(2y-x+5\right)\left(2y+x-5\right)\)
d: Ta có: \(a^2-9+6x-x^2\)
\(=a^2-\left(x-3\right)^2\)
\(=\left(a-x+3\right)\left(a+x-3\right)\)
e: Ta có: \(\left(x^2+4x+4\right)-\left(a^2-2ab+b^2\right)\)
\(=\left(x+2\right)^2-\left(a-b\right)^2\)
\(=\left(x+2-a+b\right)\left(x+2+a-b\right)\)
f: Ta có: \(x^2-2xy+y^2-z^2+2zt-t^2\)
\(=\left(x-y\right)^2-\left(z-t\right)^2\)
\(=\left(x-y-z+t\right)\left(x-y+z-t\right)\)
