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Rozklad mnohočlenů na součin - vytýkání

Rozklad mnohočlenů na součin - vytýkání. Uprav na součin:. 3abm – 6amn = 36s 4 t 2 – 48s 3 t 3 = ab 2 – ab = 3x 2 y – 9xy 2 = x 3 y 2 + 8x 3 y 3 = 105r 3 + 65r 5 = 18ab 2 + 21a 2 b 2 = 75 – 45c 3 =. Uprav na součin:. 3abm – 6amn = 3am (b – 2n)

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Rozklad mnohočlenů na součin - vytýkání

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  1. Rozklad mnohočlenů na součin - vytýkání

  2. Uprav na součin: • 3abm – 6amn = • 36s4t2 – 48s3t3 = • ab2 – ab = • 3x2y – 9xy2 = • x3y2 + 8x3y3 = • 105r3 + 65r5 = • 18ab2 + 21a2 b2 = • 75 – 45c3 =

  3. Uprav na součin: • 3abm – 6amn = 3am (b – 2n) • 36s4t2 – 48s3t3 = 12s3t2 (s – t) • ab2 – ab = ab(b – 1) • 3x2y – 9xy2 = 3xy(x – y) • x3y2 + 8x3y3 = x3y2(1 + 8y) • 105r3 + 65r5 = 5r3 (21 + 13r2 ) • 18ab2 + 21a2 b2 = 3ab(6b + 7a) • 75 – 45c3 = 15 ( 5 – 3c3)

  4. Rozlož na součin dvou činitelů: • a(x + y) + b(x + y) = • p(r + 2r) – q(r + 2r) = • x(m – n) + 5(m – n) = • 5(k – l) + (k – l) = • 2(u – 1) + v(u – 1) = • x(3z +1) + y(3z + 1) + 2z(3z + 1) = • a(u – 2) – 6b(u – 2) + (u – 2) = • 7(a2 + b) + x(a2 + b) – y(b + a2) = • 2z(x +y2 )+ (x + y2 ) – 7z(x + y2) =

  5. Rozlož na součin činitelů: • a(x + y) + b(x + y) = (x + y) (a + b) • p(r + 2r) – q(r + 2r) = (r + 2r)(p – q) • x(m – n) + 5(m – n) = (m – n) (x + 5) • 5(k – l) + (k – l) = 6 (k – l) • 2(u – 1) + v(u – 1) = (u – 1)(2 + v) • x(3z +1) + y(3z + 1) + 2z(3z + 1) = (3z + 1)(x + y+2z) • a(u – 2) – 6b(u – 2) + (u – 2) = (u – 2)(a + 6b + 1) • 7(a2 + b) + x(a2 + b) – y(b + a2) = (a2 + b)(7 + x – y) • 2z(x +y2 )+ (x + y2 ) – 7z(x + y2) = (x + y2)(1 – 5z)

  6. Z jednoho dvojčlenu vytkni -1, potom rozlož na součin dvou činitelů: • x(a – 1) + 2(1 – a) = • 4(x – y) + 7z(y – x) = • 3s(5 – r) + t(r – 5) = • a2(2a – 3) + (3 – 2a) = • q(p – 4) – r(4 – p) = • a(c – d) – b(d – c) = • a(x + y) + (– x – y) = • r2(2a – 5b) – 3s(5b – 2a)= • 3(h2 + 2q) – 4k(– h2– 2g) =

  7. Z jednoho dvojčlenu vytkni -1, potom rozlož na součin dvou činitelů: • x(a – 1) + 2(1 – a) = (a – 1) (x – 2) • 4(x – y) + 7z(y – x) = (x – y) (4 – 7z) • 3s(5 – r) + t(r – 5) = (5 – r)(3s – t) • a2(2a – 3) + (3 – 2a) = (2a – 3)(a2 - 1) • q(p – 4) – r(4 – p) = (p – 4)(q + r) • a(c – d) – b(d – c) = (c – d)(a + b) • a(x + y) + (– x – y) = (x + y)(a – 1) • r2(2a – 5b) – 3s(5b – 2a)= (2a – 5b)(r2+ 3s) • 3(h2 + 2q) – 4k(– h2– 2g) = (h2 + 2q)(3+ 4k)

  8. Doplň vhodně závorky a rozlož na součin: • y(3 + z) + 3 + z = • u(2 – v) – 2 + v = • ab(2c + d) + 2c + d = • 5x(a – 7) – a + 7 = • m2(p – 1) + p – 1 = • 3x(4 + y) – 4 – y = • rs3(t – 12) + t – 12 = • 2a2(m + n2) – m – n2 = • 8m + 3n – 2(3n + 8m) = • – y + 9z – 3x(9z – y) =

  9. Doplň vhodně závorky a rozlož na součin: • y(3 + z) + 3 + z = (3 + z)(y + 1) • u(2 – v) – 2 + v = (2 – v)(u – 1) • ab(2c + d) + 2c + d = (2c + d)(ab + 1) • 5x(a – 7) – a + 7 = (a – 7)(5x – 1) • m2(p – 1) + p – 1 = (p – 1)(m2 + 1) • 3x(4 + y) – 4 – y = (4 + y)(3x – 1) • rs3(t – 12) + t – 12 = (t – 12)(rs3 + 1) • 2a2(m + n2) – m – n2 = (m + n2)(2a2 – 1) • 8m + 3n – 2(3n + 8m) = – (3n + 8m) • – y + 9z – 3x(9z – y) = (9z – y)(1 – 3x)

  10. Rozlož na součin (postupné vytýkání): • ax + bx + cx + dx = • 5u + 5 + uv + v = • am + an + bm + bn = • 10ax + 2ay + 15bx + 3by = • pm – pq + 7m – 7q = • qr + r + q + 1 = • 2ay – 8az + 3xy – 12xz = • 5ab – 5ac + 4bc – 4c2 = • a3 - a2 + a – 1 = • y4 + y3 – y – 1 =

  11. Rozlož na součin (postupné vytýkání): • ax + bx + cx + dx = • 5u + 5 + uv + v = • am + an + bm + bn = • 10ax + 2ay + 15bx + 3by = • pm – pq + 7m – 7q = • qr + r + q + 1 = • 2ay – 8az + 3xy – 12xz = • 5ab – 5ac + 4bc – 4c2 = • a3 - a2 + a – 1 = • y4 + y3 – y – 1 =

  12. Rozlož na součin (postupné vytýkání): • ax + bx + cx + dx= 2x (a + b) • 5u + 5 + uv + v = (u + 1)(5 + v) • am + an + bm + bn= (m + n)(a + b) • 10ax + 2ay + 15bx + 3by = (5x + y)(2a + 3b) • pm – pq + 7m – 7q = (m – q)(p – 7) • qr + r + q + 1 = (q + 1)(r + 1) • 2ay – 8az + 3xy – 12xz = (y – 4z)(2a + 3x) • 5ab – 5ac + 4bc – 4c2 = (b – c)(5a + 4c) • a3 - a2 + a – 1 = (a – 1)(a2 + 1) • y4 + y3 – y – 1 = (y – 1)(y3 – 1)

  13. Zdroje: • 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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