Question

Uprosc wyrazenie:
(5x - 4y) (5x + 4y) - ¼ (10x - 2y)²

Answer 1

Skorzystamy ze wzorów skróconego mnożenia:
1) a²-b²=(a-b)(a+b)
2) (a-b)²=a²-2ab+b²

(5x - 4y) (5x + 4y) - ¼ (10x - 2y)²=(5x)²-(4y)²-¼((10x)²-2*10x*2y+(2y)²)=25x²-16y²-¼(100x²-40xy+4y²)=25x²-16y²-25x²+10xy-y²=-17y²+10xy

Answer 2

5x - 4y) (5x + 4y) - ¼ (10x - 2y)²
=25x²-16y²-¼(100x²-40xy+4y²)=
=25x²-16y²-25x²+10xy-y²=
-17y²+10xy=y(-17y+10x)

Answer 3

(5x - 4y) (5x + 4y) - ¼ (10x - 2y)² = (25x^2 +20xy-20xy-16y^2)-1/4(100x^2-40xy+4y^2)= 25x^2-16y^2-25x^2+10xy-1y^2= -17y^2+10xy

^2- to potęga druga (do kwadratu)

Czekam na naj:P