Question

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

Answer 1

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 ).