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Násobení mnohočlenů

Násobení mnohočlenů. Roznásob:. ( x + 7 ) . 2 = z ( v + z ) = ( a – 1 ) . a = 4 . ( - n + 2 ) = (-3) . (p – q) = ( 2u + 3 ) . 5v = ( -r + s ) . (-t) = 5 . (p – q + 2 ) = ( 2r 2 + 3rs - s 2 ).(-5ax) = (1 + 3a 2 x – 4ax 3 ) . (-5ax) =. Výsledky:. ( x + 7 ) . 2 = 2x + 14

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Násobení mnohočlenů

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  1. Násobení mnohočlenů

  2. Roznásob: • ( x + 7 ) . 2 = • z ( v + z ) = • ( a – 1 ) . a = • 4 . ( - n + 2 ) = • (-3) . (p – q) = • ( 2u + 3 ) . 5v = • ( -r + s ) . (-t) = • 5 . (p – q + 2 ) = • ( 2r2 + 3rs - s2 ).(-5ax) = • (1 + 3a2x – 4ax3) . (-5ax) =

  3. Výsledky: • ( x + 7 ) . 2 = 2x + 14 • z ( v + z ) = zv + z2 • ( a – 1 ) . a = a2 - a • 4 . ( - n + 2 ) = - 4n + 8 • (-3) . (p – q) = - 3p + 3q • ( 2u + 3 ) . 5v = 10uv + 15v • ( -r + s ) . (-t) = rt - st • 5 . (p – q + 2 ) = 5p – 5q + 10 • ( 2r2 + 3rs - s2 ).(-5ax) = – 10axr2 – 15arsx + 5axs2 • (1 + 3a2x – 4ax3) . (-5ax) = – 5ax – 15a3x2 + 20a2x4

  4. Roznásob závorku: • (2a3 + 5a2 – a – 6 ) . 5a = • (– 8r + 3s ) . (– 1) = • (– ab + 4b ). (– a2 ) = • (– 4a2x – 2a – x2 ) . ( - 3x ) = • (– 2pq) . ( -p2 – 6pq + 4q2) = • ( x4 – 2x3 + 0,2x2 – x + ) (– 5x ) = • 10 . ( a2 + 3ab – b + 0,01 ) = • (- 10ax) . ( - 0,3a3 + a2 – 0,1ax + 0,01x2 ) =

  5. Výsledky: • (2a3 + 5a2 – a – 6 ) . 5a = 10a4 + 25a3 – 5a2 – 30a • (– 8r + 3s ) . (– 1) = 8r – 3s • (– ab + 4b ). (– a2 ) = ab3 – 4a2b • (– 4a2x – 2a – x2 ) . (– 3x ) = 12a2x2 + 6ax + 3x3 • (– 2pq) . (– p2 – 6pq + 4q2) = 2p3q + 12p2q2 – 8pq3 • ( x4 – 2x3 + 0,2x2 – x + ) (– 5x ) = = – 2,5x5 + 10x4 – x3 + 10x2– 3x 7. 10 . (a2 + 3ab – b + 0,01) = 10a2 + 30ab - 3b + 0,1 • (– 10ax) . (– 0,3a3 + a2 – 0,1ax + 0,01x2 ) = = 3a4x – 2a3x + a2x2 – 0,1ax3

  6. Vypočti: 1. 3(a + b) – 2(a – b) = • 2 + 5(z – 1) – 3z = • ( - 2a) . ( - a2 + 3 a – 1) + 7a2 = • (x + y) . x – y(x – y) = • 5(u + 2v) – (3u – v).4 = • 2(m – 4) + (m + 3) = • 8(a – m) – 3(a + m) – 4a + 10m = • ( - 5a) . (-a +b) – a(3 + 4a – b ) =

  7. Výsledky: 1. 3(a + b) – 2(a – b) = a + 5b • 2 + 5(z – 1) – 3z = - 3 + 2z • ( - 2a) . ( - a2 + 3 a – 1) + 7a2 = 2a3 – 7a2 + 2a • (x + y) . x – y(x – y) = x2 - xy • 5(u + 2v) – (3u – v).4 = - 7u + 14v • 2(m – 4) + (m + 3) = 2m - 7 • 8(a – m) – 3(a + m) – 4a + 10m = a + 15m • ( - 5a) . (-a +b) – a(3 + 4a – b ) = a2 - 4ab – 3a

  8. Vypočti: • 8(b – 2) – 2[b – 3(4 – 2b)] = • 10x – [2(x + 1) – 3(x – 1)] + 10 = • 4x – 3[ y + 2(x – y) – x] = • 5z + 4[3z – z(2 + z) + z2] = • 2x – 5x[3 – 4(6x – 8)] = • 9z – [ 2(3z – 5) – 8] – 6 +5z = • 4a[2a(7a2 – 5a – 9)] – 4a3 =

  9. Výsledky: • 8(b – 2) – 2[b – 3(4 – 2b)] = 8 – 6b • 10x – [2(x + 1) – 3(x – 1)] + 10 = 11x + 5 • 4x – 3[ y + 2(x – y) – x] = x + y • 5z + 4[3z – z(2 + z) + z2] = 9z • 2x – 5x[3 – 4(6x – 8)] = 120x2 – 173x • 9z – [ 2(3z – 5) – 8] – 6 +5z = 8z + 12 • 4a[2a(7a2– 5a – 9)] – 4a3= = 56a4 – 44a3– 72a2

  10. Vynásob: • (m + 2).(m + 5) = • (3c + 2) . (2c + 3) = • (4 – a) . (1 + a) = • (2x + 1) . (x – 4) = • (b – 3c) . (8b + 5c) = • (3x + 5) . (– 3 – 2x) = • (2a – b) . (– b + 2a) = • (0,4u2 – 0,2v2) . ( 1,5u + 4v3) = • (– 0,4xy + y) (5xy – 4y) =

  11. Výsledky: • (m + 2).(m + 5) = m2 + 7m + 10 • (3c + 2) . (2c + 3) = 6c2 + 13c +6 • (4 – a) . (1 + a) = – a2 + 3a + 4 • (2x + 1) . (x – 4) = 2x2 – 7x - 4 • (b – 3c) . (8b + 5c) = 8b2 – 19bc – 15c2 • (3x + 5) . (– 3 – 2x) = - 6x2– 19x – 15 • (2a – b) . (– b + 2a) = 4a2 – 4ab + b2 • (0,4u2 – 0,2v2) . ( 1,5u + 4v3) = =0,6u3 – 0,3uv2 + 1,6u2v3 – 0,8v5 • (-0,4xy + y) (5xy – 4y) = – 2x2y2 + 4,1xy2 – 2y2

  12. Vypočti: 1. (x2 – 2xy + y2) ( x – y) = • (u + 5) (5 – u + 2v) = • (x + y + z) . (x + y – z) = • (4x2 + 4x – 1) (x2 – x + 2) = • (a – 2) (a – 3) (1 + a) = • (x + 6) . 3x . (x – 1) = • (r2 – 2r + 4) (r + 2) – 8r = • (3 + y) (3 – y) (y + 4) = • 3(r + 2) (2r – 4) =

  13. Výsledky: 1. (x2 – 2xy + y2) ( x – y) = x3 – 3x2y – xy2 + y3 • (u + 5) (5 – u + 2v) = 25 – u2 + 2uv + 10v • (x + y + z) . (x + y – z) = x2+ 2xy + y2 – z2 • (4x2 + 4x – 1) (x2 – x + 2) = 4 x4 + 3x2 + 9x- 2 • (a – 2) (a – 3) (1 + a) = a3 – 4a2 + a + 6 • (x + 6) . 3x . (x – 1) = 3x3 + 15x2 – 18x • (r2 – 2r + 4) (r + 2) – 8r = r3 – 8r + 8 • (3 + y) (3 – y) (y + 4) = 9y – y3 + 36 – 4y2 • 3(r + 2) (2r – 4) = 6r2 – 24

  14. Vypočti: • (x + 2) (x + 5) – (x – 1) (x – 4) = • (3x – 1)(2x + 7) – (x+1) (6x – 5) = • (5x – 2)(x + 4) – (5x2 + 32) = • 4(2x – 3y) – (3x – 2y)(2x – 3y) – 13xy = • (2x – 5x) [3 – 4(6x – 8)] = • 2x – 3[2x – 3(2x – 3)] = • 2x –3[(2x – 3)2x – 3] = • (2x – 3)[2x – 3(2x – 3)] =

  15. Vypočti: • (x + 2) (x + 5) – (x – 1) (x – 4) = 12x + 6 • (3x – 1)(2x + 7) – (x+1) (6x – 5) = 18x – 2 • (5x – 2)(x + 4) – (5x2 + 32) = 18x – 40 • 4(2x – 3y) – (3x – 2y)(2x – 3y) – 13xy = = –6x2+ 8x – 12y – 6y2 • (2x – 5x) [3 – 4(6x – 8)] = –105x + 72x2 • 2x – 3[2x – 3(2x – 3)] = 14x – 27 • 2x –3[(2x – 3)2x – 3] = 20x –12x2+ 9 • (2x – 3)[2x – 3(2x – 3)] = 30x –8x2 – 27

  16. Zdroje: • Prom.pedagogJosef Trejbal, PaeDr. Eva Kučinová, Mgr.Fantišek Vintera – Sbírka úloh z matematiky II pro 8. A 9.ročník ZŠ, SPN , r. 2000, ISBN 80-7235-111-7 • Karel Kindl – Sbírka úloh z algebry pro základní devítileté školy, SPN, Praha v roce 1979 • RNDr. Ivan Bušek, PhDr.Vlastimil Macháček, Bohumil Kotlík, Milena Tichá – Sbírka úloh z matematiky pro 8.ročník základní školy, SPN 1992, ISBN 80-04-26090-X

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