Question

Zamień poniższe sumy algebraiczne na iloczyny:

• (2b - a)(2x + y) + (a - 2b)(3x - y) =

• a² - 2ab + b² - 16 =

• 10ay - 5by + 2ax - bx =

• (a-b)x - b + a =

oraz

• (2a - 3b)² - (a + 2b)² =

• (x + 2y)² - (x - y²)² =

Dziękuje bardzo :)

Answer 1

• (2b - a)(2x + y) + (a - 2b)(3x - y) = (2b - a)(2x  +y) - (2b - a)(3x - y) = (2b - a)[2x + y  - (3x - y)] =(2b  -a)(2x  +y - 3x + y) = (2b  -a)(2y - x)

 

 

• a² - 2ab + b² - 16 = (a - b)² - 4² = (a - b - 4)(a - b + 4)

 

• 10ay - 5by + 2ax - bx = 5y(2a - b) + x(2a - b) = (2a - b)(5y + x)

 

• (a-b)x - b + a = (a - b)x + 1(a - b) = (a - b)(x + 1)

 

oraz 

 

• (2a - 3b)² - (a + 2b)² = [ (2a - 3b) - (a + 2b) ] [ ((2a - 3b) + (a + 2b) ] =

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

 

• (x + 2y)² - (x - y²)² = [ (x  +2y) - (x - y) ] [ (x + 2y) + (x - y) ] =

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