Question

Wyprowadź wzory skróconego mnożenia
(a+b)2 = (a+b) * (a+b)=
(a-b)2=(a-b) * (a-b) =
(a-b)(a+b)=

uprość:

(x+1)2-(x-1)2=
(2x+1)2+(x-2)2=

Answer 1

Wyprowadź wzory skróconego mnożenia
(a+b)2 = (a+b) * (a+b)= a²+ab+ba+b²=a²+2ab+b²
(a-b)2=(a-b) * (a-b) =a²-ab-ba+b²=a²-2ab+b²
(a-b)(a+b)=a²+ab-ba-b²=a²-b²

uprość:

(x+1)2-(x-1)2=x²+2x+1-x²+2x-1=4x
(2x+1)2+(x-2)2=4x²+4x+1+x²-4x+4=5x²+5

Answer 2

(a+b)² = (a+b) * (a+b)=a*a+a*b+b*a+b*b=a²+2*a*b+b²
(a-b)²=(a-b) * (a-b) =a*a-a*b-b*a-b*(-b)=a²-2*a*b+b²
(a-b)(a+b)=a*a+a*b-b*a-b*b=a²-b²

(x+1)²-(x-1)²=(x²+2x+1)-(x²-2x+1)=x²+2x+1-x²+2x-1=4x
(2x+1)²+(x-2)²=(4x²+4x+1)+(x²-4x+4)=4x²+4x+1+x²-4x+4=5x²+5

Answer 3

(a+b)2 = (a+b) * (a+b)= a^2+ab+ab+b^2=a^2+2ab+b^2
(a-b)2=(a-b) * (a-b) = a^2-ab-ab+b^2=a^2-2ab+b^2
(a-b)(a+b)=a^2-ab+ab-b^2=a^2-b^2

(x+1)2-(x-1)2=x^2+2x+1-(x^2-2x+1)=x^2+2x+1-x^2+2x-1=4x
(2x+1)2+(x-2)2= 4x^2+4x+1+x^2-4x+4=5x^2+5

^ do potegi