Rozklad vύrazω
1. Rozlo na souθin θinitelω:
a) m5 - m2 = 8tu 10uv = 15a3 +16a4 = x3y2 + 8x3y3 = 2n3 2n =
b) 75c 45c3 = 18ab2 + 21a2b2 = 3x2y - 9xy2 = p2q4 + q3r2 =
c) 35u3 + 56u = 20ax - 42by = 105r3 + 63r5 = 30n2 9n =
d) 7ab + 21a2b 14ab2 = 5ax + 5bx 5cx = xy3z2 x2yz3 x3y2z =
e) 3mn2 6mn + 3m = 20u4 + 32u3 4u2 = 2r5s2 14r4s3 + 10r3s4=
f) a(x + y) + b(x + y) = p(r + 2s) q(r + 2s) = x(3y + 7) (3y + 7) =
g) x( m n) + 5(m n) = (4 p) 2q(4 p) = 3d(c + ab) 8(ab + c) =
h) x(a 1) + 2(1 a) = 3s(5 r) + t(r 5) = 4(x y) + 7z(y x) =
i) q(p 4) r(4 p) = a(c d) b(d c) = y(2 x) (x 2) =
j) y(3 + z) + 3 + z = u( 2 v) 2 + v = ab(2c + d) + 2c + d =
k) 5x(a 7) a + 7 = 2a2(m + n2) m n2 = m2(p 1) + p 1 =
l) 3x(4 + y) 4 y = rs3(t 12) + t 12 = x(3y + 7) (3y + 7) =
m) q( p 4 ) r( 4 p ) = 3a( x2 3y ) 8b( 3y x2 ) = 2u( v + z ) + 3( v + z ) =
n) a2( 2a 3 ) + ( 3 2a ) =
2. Rozlo na souθin θinitelω:
a) x2 y2 = 4 a2 = b2 1 = 25a2 b2 = 9m2 64n2 = 1 x2 =
b) z2 9 = p2 49 = 100 v2 = c2d2 16 = 81p2 r2q2 =
c) x2 + 16 = 1 36u2 = 4g2h2 100x2y2 = -9 + 4c2 =
d) x4 1 = p4 25q4 = 144m2 n4 = a4 b4 = x2y4 a4b2 =
e) r3 r = z3 z5 = m5 m = 4x x3 = 2a2 8 = 5a2 20b2 =
f) 49s2 36t2 = 45 5m2 = 8x2 18y2 = 2ay2 2a3 = 7x7 28x3 =
g) 10m 25n = 15xy 10xz = ab + ab2 = 6a2 3a =
h) 5a2 125b2 = 49 m2n2 =
3. Rozlo na souθin θinitelω:
a) (a + b)2 r2 = (x y)2 1 = 25 (a + 1)2 = x2 (u + 3)2 =
b) (s 7)2 p2q2 = (2x + y)2 x2 = (m + 2)2 (2m 1)2 =
c) (a b)2 (3a + 4b)2 = (a + 5)2 (3 + a)2 = (3x y)2 (x 5y)2 =
d) x2 + 2xy + y2 = 16s2 8s + 1 = 9 + 6a + a2 = 4+x2 + 4xy + y2 =
e) p2 14p + 49 = 32 + 16x + 2x2 = 4x2 48x + 144 =
f) 45x2 + 60xy + 20y2 = 9a2 24ab + 16b2 = 49a2 + 126ab + 81b2 =
g) y2 + 1 2y = -b2 2by y2 = z2 + 9 + 6z = 1 + 4t2 4t =
h) 2mn + m2 + n2 = -20a 100 a2 = 5a2 + 10ab + 5b2 =
i) 2a2 + 12 + 18 = x2 + 2xy + y2 = 4a2 + 4ab + b2 =
j) 27x2 + 90x + 75 = 9p2 + 6pq + q2 = 25 a2b2 = 36x2 120x + 100 =
4. Rozlo na souθin θinitelω:
a) rs + ry + st + ty = 5u + 5 + uv + v =
b) qr + r + q + 1 = ax + bx + cx + dx =
c) 3a + 3b + ac + bc = a3 a2 + a 1 =