Odpowiedź:
Korzystam ze wzoru skróconego mnożenia rozwiązując te zadania:
a² - b² = ( a-b )×(a + b)
pamiętaj o odpowiednim zapisie np. 4x²=2²×x² = (2x)² , 81y² = 9²×y²= (9y)²
zad.a
25a² – (b - 2)² = (5a)² – (b - 2)² =[5a -(b-2)]×[5a+(b-2)] =(5a-b+2)×(5a+b-2)
zad.b
9x²- (x - 2)² = (3x)²- (x - 2)² =[3x-(x-2)]×[3x+(x-2)] =
= (3x-x+2)×(3x+x-2) =(2x+2)×(4x-2)
zad.c
(2x + 1)² – (x + 5)² = [2x+1 -(x+5)]×[2x+1 +(x+5)] =
= (2x+1-x-5)×(2x+1+x+5) = (x-4)×(3x+6)
zad.d
(x – 7)² – (4 – 3x)² =[x-7-(4-3x)]×[x-7+(4-3x)] =
= (x-7-4+3x)×(x-7+4-3x) = (4x-11)×(-2x -3) =
= (4x-11)× (-1)×(2x +3) = (11-4x)×(2x +3)
zad.e
25(x - 1)² – 9(2+x)² = [5×(x-1)]² - [3×(2+x)]² =
= (5x-5)² - (6+3x)² = [5x-1 -(6+3x)]×[5x-1+(6+3x)]² =
= (5x-1-6-3x)×(5x-1+6+3x) = (2x-7)×(8x+5)
zad.f
4(x + 3)² – 49(1 – x)² =[2×(x+3)]² - [7×(1-x)]² =
= (2x+6)² - (7-7x)² =[2x+6-(7-7x)]×[2x+6+(7-7x)] =
= (2x+6-7+7x)×(2x+6+7-7x) = (9x-1)×(13-5x)
