r) \(100x^2-\left(x^2-25\right)^2\)
\(=\left(10x\right)^2-\left(x^2+25\right)^2\)
\(=\left(10x-x^2-25\right)\left(10x+x^2+25\right)\)
\(=\left(-x^2+10x-25\right)\left(x^2+10x+25\right)\)
\(=-\left(x-5\right)^2\left(x+5\right)^2\)
v) \(\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y\right)^2-2\left(x+y\right)\cdot1+1^2\)
\(=\left(x+y-1\right)^2\)
y) \(12y-36-y^2\)
\(=-y^2+12x-36\)
\(=-\left(y^2-12x+36\right)\)
\(=-\left(y-6\right)^2\)
r: =(10x)^2-(x^2+25)^2
=(10x-x^2-25)(10x+x^2+25)
=-(x^2-10x+25)(x+5)^2
=-(x-5)^2(x+5)^2
t: =(2x-1)^2-(x+1)^2
=(2x-1-x-1)(2x-1+x+1)
=3x*(x-2)
v: =(x+y)^2-2(x+y)*1+1^2
=(x+y-1)^2
u: =(x-y+5)^2-2(x-y+5)*1+1^2
=(x-y+5-1)^2
=(x-y+4)^2
x: =-(x^2+2xy+y^2)
=-(x+y)^2
y: =-(y^2-12y+36)
=-(y-6)^2
t) \(\left(4x^2-4x+1\right)-\left(x+1\right)^2\)
\(=\left(2x-1\right)^2-\left(x+1\right)^2\)
\(=\left(2x-1+x+1\right)\left(2x-1-x-1\right)\)
\(=3x\left(x-2\right)\)
u) \(\left(x-y+5\right)^2-2\left(x-y+5\right)+1\)
\(=\left(x-y+5\right)^2-2\left(x-y+5\right)\cdot1+1^2\)
\(=\left(x-y+5-1\right)^2\)
\(=\left(x-y+4\right)^2\)
x) \(-x^2-2xy-y^2\)
\(=-\left(x^2+2xy+y^2\right)\)
\(=-\left(x+y\right)^2\)
