Разложите многочлен на множители 1) ас^2-ad+c^3-cd-bc^2+bd

1)          ac2-ad+c3-cd-bc2+bd=  = (ac2 – ad) + (c3 – bc2) + (bd – cd) = a·(c2 – d) + c2·(c – b) + d·(b     – c) = a·(c2 – d) + c2·(c – b) – d·(c – b) = a·(c2 – d) + c2·(c – b) – d·(c – b) = a·(c2 – d) + (c – b)·(c2 – d) = (c2 – d)·(a + c – b)

2)          mx2+my2-nx2-ny2+n-m= x2 ( m - n ) + y2 ( m - n ) - ( m - n ) = ( m-n ) (x2 + y2 - 1 )  

3)          am2+cm2-an+an2-cn+cn2= m2 (a + c ) + n2 ( a + c ) - n ( a + c ) = ( a+ c) ( m2 + n2 - n) 

4)         xy2-ny2-mx+mn+m2x-m2n= y2 ( x - n ) + m2 ( x - n) - m ( x - n ) = ( x-n) ( y2 + m2 - m ) 

5)          a2b+a+ab2+b+2ab+2=ab ( a + b + 2 )   + ( a+ b+ 2 ) = 2 ( a+ b + 2 ) 

6)          x2-xy+x-xy2+y3-y2=   x ( x –   y + 1) –   y 2 ( x –   y + 1)=( x –   y + 1)( x –   y 2 ).      

(6-x)·(6-x)-5x·(1-2x)> -(3x+4)·(3x-4)

(6-x)²-5x+10x²> -(9x²-16)

36-12x+x²-5x+10x²> -9x+16

36-17x+11x²> -9x²+16

36-17x+11x²+9x²-16> 0

20-17x+20x²> 0

20x²-17x+20> 0

20x²-17x+20=0

x∈r