: a3 53 (2b + 3)3 (2x)3 + 1 (3y2)3 x3 (9x - y) 3 103 + (5a) 3
:
a3 b3 = (a-b)(a2 + ab + b2)
a3 + b3 = (a+b)(a2 - ab + b2)
: , , .
2 b2 = (a-b)(a + b)
(a+b)2 =a2 +2 ab + b2
(a-b)2 =a2 -2 ab + b2
.
1. 36 a6 b3 96a4 b4 + 64a2b5
: 36 a6 b3 96a4 b4 + 64a2b5 = 4a2b3(9a4 24a2 b + 16b2) = 4a2b3(3a2 4b)2.
:
;
.
2. a2 + 2a b + b2 c2
: a2 + 2a b + b2 c2 = (a2 + 2a b + b2) c2 = (a + b)2 c2= (a + b c) (a + b + c)
:
;
.
3. y3 3y2 + 6y 8.
: y3 3y2 + 6y 8 = (y3 8) (3y2 -6y) = (y -2) (y2 + 2y + 4) 3y(y 2)= (y 2)(y2 + 2y + 4 3y)= (y 2)(y2 y + 4)/
:
;
;
.
, :
( ).
.
( ).
4. n3 + 3n2 + 2n.
: n3 + 3n2 + 2n = n (n2 + 3n + 2) = n (n2 + 2n + n + 2) = n ((n2 + 2n) + (n + 2)) = n (n (n + 2) + n + 2) = n (n + 1) (n + 2).
:
;
;
.
, .
. , , .
+ bx + = 0, ≠0
:
ax2 + bx + = 0 a(x x1)(x x2), x1 x2
: D = - 4ac
D > 0, . - , :
X1,2 =
D = 0, .
D < 0, .
100 .
:
1) ax2 + bx = 0;
2) ax2 + c = 0; ;
3) ax2 + c = 0; .
|
|
, :
4) a + b + c = 0;
5) a b + c = 0;
6) ;
7) ;
8) b = 2k;
9) b = 2k 1;
10) D < 0.
10 . , :
) , x;
) ;
) , , , .
.
1. * , :
a2 +4 ab + *; 9x4 6x2 y + *; 100a6 - * + b2; 4x4 25y2 =(2* -5*)(2*****)
2. : x2 x = 0 2x2 4x =0 3x2 7x = 0
3. : 532 432 1082 982 - 67 52
4. 2a + b +2a2 + ab, : a= 1; b=998; : a=45,5; b= 3; : a=7,4; b= 2
5. :
20x3 y2 + 4x2 y2; 27b3 + a6; 15a3 b +3a2 b3; 2y(x-5) + x(x-5);
b(a +5) c(a +5); 2an 5bn 10bn + am; x2 + 6x +9; 49m2 -25n2 ;
2bx - 3ay -6by + ax; 3a2 +3ab 7a -7b; a4-b4; a2 +ab 5a -5b
5a3 125ab2; a2 2ab + b2 ac + bc; 63ab3 7a2b; m2 + 6mn + 9n2 m 3n
x2 + 4x + 3; x3 + 3x2 + 4; x2 3x + 2; 12 y 3 20 y 2; x 4 1;
-5a3 -3a2 a; 4x 2y+3x2 y2+2xy2; x 3 3 x 2 y 4 xy + 12 y 2; 36 a6 b3 96a4 b4 + 64a2b5
y3 3y2 + 6y 8.
6. : (x + 3)(x + 1); (b c)(b + c) a(a + 2c); (a b)(a b c); (c a)(c + a) b(b 2a); 5a(a 5b)(a + 5b); (x2 + 3 x)(x2 + 3+ x); 7ab(9b2 a);
(m + 3n)(m + 3n 1); (b a c)(b + a + c); (c a + b)( + a b); (x 2)(x 1);
7. :a) : ) + ) :
) - ) + ) + ) - ) +
) + ) -