Question

zapsz w postaci sumy algebraicznej;

(5+x²)(√5-x)(√5+x)=

(x²+2x+4)(x-2)(x³+8)=

(x²-x+1)(x+1)(1-x³)=

uprośc wyrażenie;

(2x-1)(1+2x+4x²+8x³+16x⁴)=

(x²-1)(1+x²+x⁴+x⁸+x¹⁰+x¹²)=

Answer 1

(5+x²)(√5-x)(√5+x)=(5+x²)(5 - x²) = 25 - x⁴

 

(x²+2x+4)(x-2)(x³+8)= (x³ - 8)(x³ + 8) = x⁶ - 64

 

(x²-x+1)(x+1)(1-x³)= (1 + x³)(1 - x³) = 1 - x⁶

 

uprośc wyrażenie;

(2x-1)(1+2x+4x²+8x³+16x⁴)=2x+4x²+8x³+16x⁴+32x⁵ - 1-2x-4x²-8x³-16x⁴ = 32x⁵ - 1

 

(x²-1)(1+x²+x⁴+x⁸+x¹⁰+x¹²)= x²+x⁴+x⁶+x¹⁰+x¹²+x¹⁴ - 1-x²-x⁴-x⁸-x¹⁰-x¹² = x¹⁴ - x⁸+ x⁶ - 1