Question

Zapisz w jak najprostrzej postaci:

a) (a+3)(a-1)+(a-7)(a+5)

b) (2b-5)(3-2b)-(3b+2)(b-6)

c) -7c^2(5c-4)+(3c^2+c)(6-2c)

d) 3m(m-4)(5m+2)-m(2m+3)(4-3m)

e) -2x(3x-5y)-(x+2y)(3x-y)

Answer 1

a) (a+3)(a-1)+(a-7)(a+5) =

= (a² + 3a -a -3) + (a² + 5a - 7a - 35) =

= a² + 2a - 3 + a² -2a - 35 =

= 2a² -38

 

b) (2b-5)(3-2b)-(3b+2)(b-6) =

= (6b + 4b² - 15 + 10b) - ( 3b² - 18b + 2b - 12) =

= 6b + 4b² - 15 + 10b - 3b² + 18b - 2b + 12=

= b² + 32b -3

 

c) -7c²(5c-4)+(3c²+c)(6-2c) =

= -35c³ + 28c² + 18c² - 6 c³ + 6c - 2c²=

= -41c³ + 44c² + 6c

 

d) 3m(m - 4)(5m + 2) - m(2m + 3)(4 - 3m) =

= 3m(5m² + 2m - 20m - 8) - m(8m - 12m² + 12 - 9m) =

= 15m³ + 6m² - 60m² - 24m - 8m² + 12m³ - 12m + 9m² =

= 27m³ - 53m² - 36m

 

e) -2x(3x - 5y) - (x + 2y)(3x - y) =

= -6x² + 10xy - (3x² - xy + 6xy - 2y²) =

= -6x² + 10xy - 3x² + xy - 6xy + 2y² =

= -9x² + 5xy + 2y²

Answer 2

a)                                               a2-a do kwadratu,m2-m do kwadratu,m3-m do sześcianu                                                 

(a+3)(a-1)+(a-7)(a+5)=a2-a+3a-3+a2+5a-7a=2a2 +a-38 

b)

(2b-5)(3-2b)-(3b+2)(b-6)=6a-4ab-15+10b-3b2+18b-2b+12=6a-4ab-3+38b-3b2-2b

c)

d)

3m(m-4)(5m+2)-m(2m+3)(4-3m)=3m(5m2+2m-20m-8)-m(8m-6m2+12-9m2)=15m3+6m2-6m2-24m-8m2+6m3-12m+9m2=21m3-53m2-36m