Question

Wykonaj mnozenie i zredakuj wyrazy podobne
1. (a - 4)(a + 5) =
2. (7b + 3)(2 - 4b) =
3. (-3c + 2d)(2c - 6)=
4. (9s - 2t)(7t - s) =
5. (-10m + 3n)(5n - 4) =
6. (3kl + 8k)(4 - 2l) =
7. (4xy + 3x)(2y + 5x^2y) =
8. (-2p^2q - 3p)(5pq - 3p^2q^2)

W 7 i 8 jest np. "5x^2" to oznacza ze 5x jest do potegi 2 ;)

Zapisz w jak najprostrzej postaci
1. (a+3)(a-1)+(a-7)(a+5)
2. (2b-5)(3-2b)-(3b+2)(b-6)
3. -7c^2(5c-4)+(3c^2+c)(6-2c)
4. 3m(m-4)(5m+2)-m(2m+3)(4-3m)
5. -3x(3x-5y)-(x+2y)(3x-y)

Answer 1

1. (a - 4)(a + 5) = a² - 4a + 5a - 20 = a² + a - 20
2. (7b + 3)(2 - 4b) = 14b + 6 - 28b² - 12b = - 28b² + 2b + 6
3. (-3c + 2d)(2c - 6)= - 6c² + 4cd +  18c - 12d
4. (9s - 2t)(7t - s) = 63 st - 14 t² - 9 s² + 2st = -9s² - 14 t² + 65 st
5. (-10m + 3n)(5n - 4) = - 50 mn + 15n² + 40 m - 12 n = 15n² + 40m - 12n - 50mn
6. (3kl + 8k)(4 - 2l) = 12kl + 32k - 6kl² - 16 kl = - 6kl² - 4kl + 32k
7. (4xy + 3x)(2y + 5x²y) = 8 xy² + 6xy + 20x³ y² + 15x³ y
8. =

Zapisz w jak najprostszej postaci
1.
(a+3)(a-1)+(a-7)(a+5) = a²+ 3a - a - 3 + a² - 7a + 5a - 35 = 2a² - 38
2.
(2b-5)(3-2b)-(3b+2)(b-6) = ( 6b - 15 - 4b² + 10b) -( 3b² + 2b - 18b - 12) =
6b - 15 - 4b² + 10b - 3b² - 2b + 18b + 12 =  - 7b²  + 32b - 3

3.
 -7c²(5c-4)+(3²+c)(6-2c) =  - 35 c³ + 28 c² + 18c² + 6c - 12c³ - 2c²= - 47c³ + 44c² + 6c

4.
3m(m-4)(5m+2)-m(2m+3)(4-3m) =
3m² -12m)( 5m + 2) - ( 2m² + 3m)( 4 - 3m)=
( 15m³ - 60m² + 6m² - 24) -( 8m² + 12m - 6m³ - 9m²) =
15m³ - 60m² + 6m² - 24) -8m² - 12m + 6m³  + 9m² =
21m³ - 71m² - 36m

5.
 -3x(3x-5y)-(x+2y)(3x-y) = - 9x² + 15xy  - ( 3x² + 6xy - xy - 2y²) =
- 9x² + 15xy - 3x² - 6xy + xy + 2y² = - 12x² + 2y² + 10xy