\(a.x^2-y^2\\ =\left(x+y\right)\left(x-y\right)\\ b.\left(x-2\right)^2-4\\ =\left(x-2\right)^2-2^2\\ =\left(x-2-2\right)\left(x-2+2\right)\\ =x\left(x-4\right)\\ b.\left(3x+1\right)^2-\left(x-3\right)^2\\ =\left(3x+1-x+3\right)\left(3x+1+x-3\right)\\ =\left(2x+4\right)\left(4x-2\right)\\ d.16\left(x-3\right)^2-25\left(x+5\right)^2\\ =\left[4\left(x-3\right)\right]^2-\left[5\left(x+5\right)\right]^2\\ =\left(4x-12\right)^2-\left(5x+25\right)^2\\ =\left(4x-12-5x-25\right)\left(4x-12+5x+25\right)\\ =\left(-x-37\right)\left(9x+13\right)\)
a: \(x^2-y^2=\left(x-y\right)\left(x+y\right)\)
b: \(\left(x-2\right)^2-4=\left(x-2-2\right)\left(x-2+2\right)\)
=x(x-2)
c: \(\left(3x+1\right)^2-\left(x-3\right)^2\)
\(=\left(3x+1+x-3\right)\cdot\left(3x+1-x+3\right)\)
=(4x-2)(2x+4)
\(=2\left(2x-1\right)\cdot2\left(x+2\right)=4\left(2x-1\right)\left(x+2\right)\)
d: \(16\left(x-3\right)^2-25\left(x+5\right)^2\)
\(=\left(4x-12\right)^2-\left(5x+25\right)^2\)
\(=\left(4x-12-5x-25\right)\left(4x-12+5x+25\right)\)
=(-x-37)(9x+13)
=-(x+37)(9x+13)
e: \(x^2+4x+4-y^2\)
\(=\left(x^2+4x+4\right)-y^2=\left(x+2\right)^2-y^2\)
=(x+2+y)(x+2-y)
f: \(\left(x-3\right)^2-4\cdot\left(x-3\right)+4\)
\(=\left(x-3\right)^2-2\cdot\left(x-3\right)\cdot2+2^2\)
\(=\left(x-3-2\right)^2=\left(x-5\right)^2\)
g: \(x^2-y^2-2y-1=x^2-\left(y^2+2y+1\right)\)
\(=x^2-\left(y+1\right)^2=\left(x-y-1\right)\left(x+y+1\right)\)
\(e.x^2+4x+4-y^2\\ =\left(x^2+4x+4\right)-y^2\\ =\left(x+2\right)^2-y^2\\ =\left(x+2-y\right)\left(x+2+y\right)\\ f.\left(x-3\right)^2-4\left(x-3\right)+4\\ =\left(x-3\right)^2-2\cdot\left(x-3\right)\cdot2+2^2\\ =\left(x-3-2\right)^2\\ =\left(x-5\right)^2\\ g.x^2-y^2-2y-1\\ =x^2-\left(y^2+2y+1\right)\\ =x^2-\left(y+1\right)^2\\ =\left(x-y-1\right)\left(x+y+1\right)\)
`a)x^2-y^2=(x-y)(x+y)`
`b)(x-2)^2-4`
`=(x-2)^2-2^2`
`=(x-2-2)(x-2+2)`
`=x(x-4)`
`c)(3x+1)^2-(x-3)^2`
`=(3x+1-x+3)(3x+1+x-3)`
`=(2x+4)(4x-2)`
`=4(x+2)(2x-1)`
`d)16(x-3)^2-25(x+5)^2`
`=[4(x-3)]^2-[5(x+5)]^2`
`=(4x-12-5x-25)(4x-12+5x+25)`
`=(-x-37)(9x+13)`
`e)x^2+4x+4-y^2`
`=(x+2)^2-y^2`
`=(x+2-y)(x+y+2)`
`f)(x-3)^2-4(x-3)+4`
`=(x-3-2)^2`
`=(x-5)^2`
`g)x^2-y^2-2y-1`
`=x^2-(y^2+2y+1)`
`=x^2-(y+1)^2`
`=(x-y-1)(x+y+1)`
a, \(x^2-y^2=\left(x-y\right)\left(x+y\right)\)
b, \(\left(x-2\right)^2-4=\left(x-2\right)^2-2^2=x\left(x-4\right)\)
c, \(\left(3x+1\right)^2-\left(x-3\right)^2=\left(3x+1-x+3\right)\left(3x+1+x-3\right)=\left(2x+4\right)\left(4x-2\right)\)
d, \(16\left(x-3\right)^2-25\left(x+5\right)^2=\left(4x-12\right)^2-\left(5x+25\right)^2=\left(4x-12-5x-25\right)\left(4x-12+5x+25\right)=\left(-x-37\right)\left(9x+13\right)\)
e, \(x^2+4x+4-y^2=\left(x+2\right)^2-y^2=\left(x+2-y\right)\left(x+2+y\right)\)
f, \(\left(x-3\right)^2-4\left(x-3\right)+4=\left(x-3-2\right)^2=\left(x-5\right)^2\)
g, \(x^2-y^2-2y-1=x^2-\left(y+1\right)^2=\left(x-y-1\right)\left(x+y+1\right)\)
