1) \(x^2-25\)
\(=x^2-5^2\)
\(=\left(x-5\right)\left(x+5\right)\)
2) \(9x^2-\dfrac{1}{16}y^2\)
\(=\left(3x\right)^2-\left(\dfrac{1}{4}y\right)^2\)
\(=\left(3x-\dfrac{1}{4}y\right)\left(3x+\dfrac{1}{4}y\right)\)
3) \(x^6-y^4\)
\(=\left(x^3\right)^2-\left(y^2\right)^2\)
\(=\left(x^3-y^2\right)\left(x^3+y^2\right)\)
4) \(\left(2x-5\right)^2-64\)
\(=\left(2x-5\right)^2-8^2\)
\(=\left(2x-5-8\right)\left(2x-5+8\right)\)
\(=\left(2x-13\right)\left(2x+3\right)\)
5) \(81-\left(3x+2\right)^2\)
\(=9^2-\left(3x+2\right)^2\)
\(=\left(9-3x-2\right)\left(9+3x+2\right)\)
\(=\left(7-3x\right)\left(3x+11\right)\)
6) \(9\left(x-5y\right)^2-16\left(x+y\right)^2\)
\(=\left[3\left(x-5y\right)\right]^2-\left[4\left(x+y\right)\right]^2\)
\(=\left(3x-15y-4x-4y\right)\left(3x-15y+4x+4y\right)\)
\(=\left(-x-19y\right)\left(8x-11y\right)\)
7: x^3-8
=x^3-2^3
=(x-2)(x^2+2x+4)
8: 27x^3+125y^3
=(3x)^3+(5y)^3
=(3x+5y)(9x^2-15xy+25y^2)
9: x^6+216
=(x^2)^3+6^3
=(x^2+6)(x^4-6x^2+36)
10: x^2+8x+16=(x+4)^2
11: 9x^2-12xy+4y^2=(3x-2y)^2
12: =-(25x^2y^2-10xy+1)=-(5xy-1)^2
13: =x^3-3*x^2*2+3*x*2^2-2^3
=(x-2)^3
14: =(2x)^3+3*(2x)^2*y+3*2x*y^2+y^3
=(2x+y)^3
15: \(=2xy\left(x^2+y^2+2xy-1\right)\)
\(=2xy\left[\left(x+y\right)^2-1\right]\)
=2xy(x+y+1)(x+y-1)
16: =(x-y)^2+4(x-y)
=(x-y)(x-y+4)
17: =x^3+3x^2y+3xy^2+y^3-x-y
=(x+y)^3-(x+y)
=(x+y)[(x+y)^2-1]
=(x+y)(x+y+1)(x+y-1)
18: =(x-y)^2-4z^2
=(x-y-2z)(x-y+2z)
19: =x^2-y^2-(x+y)
=(x+y)(x-y)-(x+y)
=(x+y)(x-y-1)
20: =(x-y)^2-z^2
=(x-y-z)(x-y+z)
