Практические задания Вынесение общего множителя за скобки

7 класс. Вынесение общего множителя за скобки

1 вариант

1 тип. 1) 8х + 8у = 8(х + у) 2) 5х – xz = x(5 – z) 3) 4n – 4 = 4n - 4∙1 = 4(n – 1)

15х + 15у = bc + bx = 6y – 6 =

21к – 21t = 10xy – ym = 7z + 7 – 7x =

0,4a – 0,4b + 0,4n =

2 тип. 1) – 8x – 8y = 8(- x – y) 2) – 8x – 8y = - 8(x +y) [ – 8x – 8y = - 8x + (- 8y) ]

-11d - 11c = -11d - 11c =

- xa – xb = - xa – xb =

3 тип. 1) 15х + 25у = 5(3х + 5у), [ НОД(15, 25) = 5 ]

2) 3c + 21d – 30x = 3(c + 7d -10x)

5x + 5y = 9x – 12t =

12y - 18z + 30x = 8b - 8k – 24x =

4 тип. 1) 12xy - 18yxz +9yz = 3y(4x – 6xz + 3z)

2) 12xy – 7yxz + 9yz = y(12x – 7xz + 9z)

6xy + 10xz = 22bc – 11c =

8nd + 16nk – 8mn = 15nk – 20xk + 10xky =

14xz – 5yz – 11mz =

5 тип. 1) 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

2) 2x(x + 2) + 5(2 + x) = 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

3) 2x(x - 2) + 5(x – 2) = (x – 2)(2x + 5)

4) 2x(x - 2) + 5(2 - x) = 2x(x - 2) - 5(x - 2) = (x – 2)(2x - 5) [ 5 – 2 = 3; 2 – 5 = - 3 ]

5y(2x + 4) + x(2x + 4) = 13(y – 8) – z(y – 8) =

4y(2x + 1) + x(1 + 2x) = z(2y – 5) – 12(5 – 2y) =

6 тип. a⁵ + a³ + a² = a∙a∙a∙a∙a + a∙a∙a + a∙a∙1 = a² (a³ + a + 1)

x⁷ + x³ – x⁴ = c³ + c⁵ – c + c⁴ =

7 тип. 1) 4y⁴ – 8y² + 6y = 2y(2y³ – 4y + 3)

2) 5x⁴y² + 20x³y⁵ – 25x⁶y² = 5x³y² (3x + 4y³ – 5x³)

3) 12ab⁴ – 18a²b³c = 6ab³(2b – 3ac)

15a⁴b² + 6a²b³ = 9y⁴ + 21y⁵ – 30y⁷ =

- 20xy² – 24x²y + 45x²y² =

8 тип. 1) (x – 2)² + (x – 2) = (x – 2)(x – 2) + (x – 2)∙1 = (x – 2)(x - 2 + 1) = (x – 2)(2x - 1) =

2) (x – 2)² + x(x – 2) = (x – 2)(x – 2) + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

3) (2 - x)² + x(x – 2) = (x - 2)² + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

4) 14(x – 2)² + x(x – 2) = (x – 2)∙(14(x – 2) + x) = (x – 2)(14x – 28 + x) = (x – 2)(15x – 28)

(2m + 3) + 5(2m + 3)² =

2y(y +3) + 6(3+ y)² =

-3(2x +1)² - (2x + 1) =

5(4 – z)² – 4(4 – z) =

y(2y – 7) + 2(7 – 2y)² =

7 класс. Вынесение общего множителя за скобки

2 вариант

1 тип. 1) 8х + 8у = 8(х + у) 2) 5х – xz = x(5 – z) 3) 4n – 4 = 4n - 4∙1 = 4(n – 1)

14х + 14z = by + yx = 3y – 3 =

10y – 10t = 7xy – yz = 11z + 11x – 11 =

0,8a + 0,8b - 0,8m =

2 тип. 1) – 8x – 8y = 8(- x – y) 2) – 8x – 8y = - 8(x +y) [ – 8x – 8y = - 8x + (- 8y) ]

-12d – 12m = -12d – 12m =

- ma – mb = - ma – mb =

3 тип. 1) 15х + 25у = 5(3х + 5у), [ НОД(15, 25) = 5 ]

2) 3c + 21d – 30x = 3(c + 7d -10x)

4g + 2f = 9x – 6y =

12y + 18z – 24k = 7d - 7k – 21x =

4 тип. 1) 12xy - 18yxz +9yz = 3y(4x – 6xz + 3z)

2) 12xy – 7yxz + 9yz = y(12x – 7xz + 9z)

8xy + 10yz = 30xy – 15y =

6kd + 14nk – 8mk = 10pk – 15xp + 10xpy =

11xz +5yz – 17mz =

5 тип. 1) 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

2) 2x(x + 2) + 5(2 + x) = 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

3) 2x(x - 2) + 5(x – 2) = (x – 2)(2x + 5)

4) 2x(x - 2) + 5(2 - x) = 2x(x - 2) - 5(x - 2) = (x – 2)(2x - 5) [ 5 – 2 = 3; 2 – 5 = - 3 ]

6y(2x - 5) + x(2x - 5) = 13(y – 10) – z(y – 10) =

4y(3y + 1) + x(1 + 3y) = z(4y – 7) – 12(7 – 4y) =

6 тип. a⁵ + a³ + a² = a∙a∙a∙a∙a + a∙a∙a + a∙a∙1 = a² (a³ + a + 1)

y⁷ + y⁵ – y³ = x⁴ - x⁵ – x + x⁶ =

7 тип. 1) 4y⁴ – 8y² + 6y = 2y(2y³ – 4y + 3)

2) 5x⁴y² + 20x³y⁵ – 25x⁶y² = 5x³y² (3x + 4y³ – 5x³)

3) 12ab⁴ – 18a²b³c = 6ab³(2b – 3ac)

18a⁴b³ + 6ab³ = 4by³ + 8b²y² – 32b³y⁴ =

- 24xy³ + 18x²y - 36x²y² =

8 тип. 1) (x – 2)² + (x – 2) = (x – 2)(x – 2) + (x – 2)∙1 = (x – 2)(x - 2 + 1) = (x – 2)(2x - 1) =

2) (x – 2)² + x(x – 2) = (x – 2)(x – 2) + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

3) (2 - x)² + x(x – 2) = (x - 2)² + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

4) 14(x – 2)² + x(x – 2) = (x – 2)∙(14(x – 2) + x) = (x – 2)(14x – 28 + x) = (x – 2)(15x – 28)

(2n + 5) + 4(2n + 5)² =

3y(y +7) + 5(7 + y)² =

-3(2x +4)² - (2x + 4) =

5(z – 2)² – 6(z – 2) =

x(3y – 3) + 2(3 – 3y)² =

7 класс. Вынесение общего множителя за скобки

3 вариант

1 тип. 1) 8х + 8у = 8(х + у) 2) 5х – xz = x(5 – z) 3) 4n – 4 = 4n - 4∙1 = 4(n – 1)

18х + 18y = xy - zx = 15y – 15 =

11y – 11z = 4xy + yz = 5z + 5p – 5 =

0,9a + 0,9b - 0,9c =

2 тип. 1) – 8x – 8y = 8(- x – y) 2) – 8x – 8y = - 8(x +y) [ – 8x – 8y = - 8x + (- 8y) ]

-14k – 14w = -14k – 14w =

- mc – mb = - mc – mb =

3 тип. 1) 15х + 25у = 5(3х + 5у), [ НОД(15, 25) = 5 ]

2) 3c + 21d – 30x = 3(c + 7d -10x)

4x + 2y= 15x – 6z =

20y - 16z + 24m = 8d + 8k –16y =

4 тип. 1) 12xy - 18yxz +9yz = 3y(4x – 6xz + 3z)

2) 12xy – 7yxz + 9yz = y(12x – 7xz + 9z)

10xy + 15yz = 35xy – 15x =

6kx – 14yk – 8mk = 6ab – 3b + 12abc =

13yz +5yx – 19mz =

5 тип. 1) 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

2) 2x(x + 2) + 5(2 + x) = 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

3) 2x(x - 2) + 5(x – 2) = (x – 2)(2x + 5)

4) 2x(x - 2) + 5(2 - x) = 2x(x - 2) - 5(x - 2) = (x – 2)(2x - 5) [ 5 – 2 = 3; 2 – 5 = - 3 ]

6z(2x - 8) + x(2x - 8) = 11(y – 12) – y(y – 12) =

5a(4y + 1) – 4b(1 + 4y) = c(4a – b) – b(b – 4a) =

6 тип. a⁵ + a³ + a² = a∙a∙a∙a∙a + a∙a∙a + a∙a∙1 = a² (a³ + a + 1)

y⁸ + y⁴ – y³ = z⁴ - z⁵ + z + z² =

7 тип. 1) 4y⁴ – 8y² + 6y = 2y(2y³ – 4y + 3)

2) 5x⁴y² + 20x³y⁵ – 25x⁶y² = 5x³y² (3x + 4y³ – 5x³)

3) 12ab⁴ – 18a²b³c = 6ab³(2b – 3ac)

28x⁴b³ + 21x³b² = 4zy³ – 8z²y² – 18z³y⁴ =

- 20xy³ + 18x³y² - 30x²y =

8 тип. 1) (x – 2)² + (x – 2) = (x – 2)(x – 2) + (x – 2)∙1 = (x – 2)(x - 2 + 1) = (x – 2)(2x - 1) =

2) (x – 2)² + x(x – 2) = (x – 2)(x – 2) + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

3) (2 - x)² + x(x – 2) = (x - 2)² + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

4) 14(x – 2)² + x(x – 2) = (x – 2)∙(14(x – 2) + x) = (x – 2)(14x – 28 + x) = (x – 2)(15x – 28)

(2k + 7) + 3(2k + 7)² =

4y(y +11) - 5(11 + y)² =

-5(3x +1)² - (3x + 1) =

5(a – 6)² – 8(a – 6) =

x(6y – 3) + 4(3 – 6y)² =

7 класс. Вынесение общего множителя за скобки

4 вариант

1 тип. 1) 8х + 8у = 8(х + у) 2) 5х – xz = x(5 – z) 3) 4n – 4 = 4n - 4∙1 = 4(n – 1)

9х + 9y = ad – 10d = 12x – 12 =

25y – 25z = mn + mt = 6y + 6p – 6 =

0,21m + 0,21n - 0,21k=

2 тип. 1) – 8x – 8y = 8(- x – y) 2) – 8x – 8y = - 8(x +y) [ – 8x – 8y = - 8x + (- 8y) ]

-10x – 10y = -10x – 10y =

- na – nb = - na– nb =

3 тип. 1) 15х + 25у = 5(3х + 5у), [ НОД(15, 25) = 5 ]

2) 3c + 21d – 30x = 3(c + 7d -10x)

12x + 18z = 15x – 21y =

20x + 12z – 28y = 9h + 27d –15y =

4 тип. 1) 12xy - 18yxz +9yz = 3y(4x – 6xz + 3z)

2) 12xy – 7yxz + 9yz = y(12x – 7xz + 9z)

30xy + 15xz = 25xy – 15y =

6yx – 10yk + 14my = 27ab – 3a + 12abc =

11az + 7ax – 17ay =

5 тип. 1) 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

2) 2x(x + 2) + 5(2 + x) = 2x(x + 2) + 5(x + 2) = (x + 2)(2x + 5)

3) 2x(x - 2) + 5(x – 2) = (x – 2)(2x + 5)

4) 2x(x - 2) + 5(2 - x) = 2x(x - 2) - 5(x - 2) = (x – 2)(2x - 5) [ 5 – 2 = 3; 2 – 5 = - 3 ]

6m(10x - 7) + x(10x - 7) = 12(x – 4) – y(x – 4) =

5a(2y + 8) – 3b(8 + 2y) = a(3a – 2b) – b(2b – 3a) =

6 тип. a⁵ + a³ + a² = a∙a∙a∙a∙a + a∙a∙a + a∙a∙1 = a² (a³ + a + 1)

z⁶ + z⁴ – z² = a⁴ + a⁵ - a + a² =

7 тип. 1) 4y⁴ – 8y² + 6y = 2y(2y³ – 4y + 3)

2) 5x⁴y² + 20x³y⁵ – 25x⁶y² = 5x³y² (3x + 4y³ – 5x³)

3) 12ab⁴ – 18a²b³c = 6ab³(2b – 3ac)

28x⁴b³ + 21x³b² = 4zy³ – 8z²y² – 18z³y⁴ =

- 20xy³ + 18x³y² - 30x²y =

8 тип. 1) (x – 2)² + (x – 2) = (x – 2)(x – 2) + (x – 2)∙1 = (x – 2)(x - 2 + 1) = (x – 2)(2x - 1) =

2) (x – 2)² + x(x – 2) = (x – 2)(x – 2) + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

3) (2 - x)² + x(x – 2) = (x - 2)² + x(x – 2) = (x – 2)(x - 2 + x) = (x – 2)(2x - 2∙1) =

= (x – 2)∙2∙(x – 1) = 2(x – 2)(x – 1)

4) 14(x – 2)² + x(x – 2) = (x – 2)∙(14(x – 2) + x) = (x – 2)(14x – 28 + x) = (x – 2)(15x – 28)

(2x + 1) + 4(2x + 1)² =

4y(y + 9) – 5(9 + y)² =

-7(3z +11)² - (3z + 11) =

5(n– 2)² – 6(n – 2) =

y(3y – 3) + 2(3 – 3y)² =