Question

Zapisz w jak najprostszej postaci:

(2a-1)(2a+1)-(a+1)²

3x²-(x-3)(x+3)

(x²+5)(x²-5)+(x²-1)²

x(2x-1)²-2x(x-1)(x+1)

Answer 1

a)

(2a-1)(2a+1)-(a+1)²=4a²-1-(a²+2a+1)=4a²-1-a²-2a-1= 3a²-2a-2

 

b)

3x²-(x-3)(x+3)=3x²-(x²-9)=3x²-x²+9= 2x²+9

 

c)

(x²+5)(x²-5)+(x²-1)²=x⁴-25+x⁴-2x²+1= 2x⁴-2x²-24

 

d)

x(2x-1)²-2x(x-1)(x+1)=x(4x²-4x+1)-2x(x²-1)=4x³-4x²+x-2x³+2x= 2x³-4x²+3x