1) 17m²n-5n²m=nm(17m-5n)
2) 20a³-6b²-24ab+5a²b=4a(5a²-6b)+b(6b-5a²)=4a(5a²-6b)+b(5a²-6b²)=(5a²-6b)(4a+b)
3) 2x²-4xy²+3xy-6y³=-2y²(2x+3y)+x(2x+3y)=(2x+3y)(-2y²+x) при x=1/4, y=1/6
(2*1/4+3*1/6)(-2*1/6+1/4)=(1/2+1/2)(-2*1/36+1/4)=1(-1/18+1/4)=4/72+18/72=14/72=7/36.
4) а) 16x⁴-0.09a²=(4x²)²-(0.3a)²=(4x²-0.3a)(4x²+0.3a)
б) 4a⁶b²-20a³bc²+25c⁴=(2a³b-5c²)²=(2a³b-5c²)(2a³b-5c²)
в)1/16a²+1/6ab+1/9b²=(1/4a+1/3b)²=(1/4a+1/3b)(1/4a+1/3b)
5) (x-2y)³+(x+2y)³=(x-2y+x+2y)((x-2y)²-(x-2y)(x+2y)+(x+2y)²)=2x(x²-4xy+4y²-(x²-(2y²))+x²+4xy+4y²)=2x(2x²+8y-x²+4y²)=2x(x²+12y²)
6) 128²-78²=(128-78)(128+78)=50*206=10300
7) 108³-7³=(108-7)(108²-108*7+7²)=101(108²-108*7+7²) - кратно 101
8) а)a³+b³/b²-a²=a+b
б)3a³b²-18a²b³+27ab⁴/6a³b-18a²b²=b-b+27ab⁴/2=27ab⁴/2