Тренажёр по математике по теме "Формулы сокращённого умнажения"

1. Представить в форме многочлена стандартного вида:

(b-a)²                                                            (m+n)²                                                      (x-b)²                                                                              

(c+d)²                                      (x+y) ²                                                       (d+n)²

(-x+y)²                                                        (-m+y) ²                                                    (-a+c)²

(x+2)²                                                          (n-3)²                                                          (n+5)²

(a-3) ²                                            (d+5)²                                    (m-3)²

(2a-3b)²                                                      (3c-4d)²                                                    (7a-3c)²

(-4x-5)²                                                       (-5-2x)²                                                     (-5n-3)²

(5x-b)²                                                          (3y² –x )²                                                 (4m² -n)²

(3a³+6b⁴)²                                                  (2m⁴+3n³)²                                     (9a² +2n⁵)²                        

2. Представить трёхчлен в виде квадрата двучлена:

x²+ 2xy+y²                                                 a² –2ab+b²                                               m² +2mn+n²

m²-2mn+n²                                                c² +2cd+d²                                                x² -2xy+y²

a² – 4a+4                                   m² +6m+9                              c²-8c+16                                                                                                                               

9b² +6bc+c²                                                4x²  + 4xy+y²                                       25a² +10ab+b²

 4a² -12ab+9b²                                          9b²  +24bc+16c²                                9x²-18xy+9y ²

0,25x²+xy+y²                                            0,64m² – 1,6nm+n²                          0,36c²+1,2cd+d²

a⁴ +4a² b³ +4b⁶                                           a⁸ -6a⁴ b² +9b⁴                                      m⁶ +8m³ n⁴ +16n⁸

9c⁶ -24c³d⁴+16d⁸                                     4c⁸+ 12c⁴ d³ +9d⁶                                  16x⁶ -16x³ y⁴ +4y⁸

3. Представить произведение в виде многочлена:

(x-4)(x+4)                                  (a-2)(a+2)                           (c+3)(c-3)

(5-2a)(5+2a)                               (3-2b)( 3+2b)                      (4-3n)(4+3n)

(3x+2y)(3x-2y)                           (2m+7n)( 2m-7n)               (9m-2c)(9m+2c)

(a-8b)(8b+a)                               (x-5y)(5y+x)                       (c-7d)(7d+c)

(0,2n+3m)( 0,2n-3m)                 (0,5d+2c)( 0,5d-2c)            (0,4x+5y)(0,4x-5y)

(-2a-0,5b)(0,5b-2a)                    (-4a-0,5b)(0,5b-4a)            (-5m-0,2n)(0,2n-5m)

(x³-y²)( x³+y²)                           (m²+n⁵)( m²-n⁵)                  (a³-b⁵)( a³+b⁵)

(5a⁴+8b⁵)( 8b⁵-5a⁴)                    (2c³+5d⁴)(5d⁴-2c³)             (2n⁷+6m³)(6m³-2n⁷)

4.Разложить на множители:

d²-m²                                                                   c²-d²                                                         d²-b²

x²-4                                           n²-9                                   n²-16

a²-36b²                                                               25b²-16c²                                            4n²-25m²

0,25x²-0,09z²                                               0,36m²-0,04z²                                 0,81x² – 0,64y²

0,04a²-0,01b²                                               0,04c²-0,81b²                                   0,49c²-0,01b²

9a⁴-16b⁶                                                           81n⁶-49m⁴                                          9a⁴-25n⁶

64a²b⁴-49c⁸d¹⁰                                            25c⁴d¹⁰-64a⁶b⁸                                64c⁴b⁴-9d⁸n¹⁰

0,81y¹⁴-25z¹⁶                                                0,01b¹⁶-36d¹⁴                                   16n¹⁰-0,25c¹⁴

a² –(3a+b)²                                                     n²-(2a²+n)²                                         b² – (3c+b)²

(b⁶+b⁴ )²-b⁸                                                     (c⁶+d³)2-d⁶                                         (m³+d⁵)²-d¹⁰     

 a⁴-1                                              b⁴-81                                 16-c⁴

 36a³-a                                       b-100b³                                                9n-n³

 m² -x² -6x-9                                 c²-x²+4x-4                         a² -x²+6x-9

Краткое описание документа:

Задания тренажёра можно предлагать как для индивидуальной, так и для коллективной работе в классе. По ним можно проводить математические эстафеты: ученики по очереди записывают ответы (по необходимости можно больше внимания уделять развитию устной речи школьников). Возможна работа в парах, когда один ученик называет ответы, а второй второй проверяет их правильность. Задания тренажёра можно использовать многократно, на разных этапах урока.