Question

Pomocy na jutro Matematyka 1 nowa era str.82 zad 1,2 Oblicz

A (2+√2)³

B (√5-1)³

C (3-√3)³

D (√2-4)³

E (1+2√5)³

F (2√3-3)³

G (√2+√3)³

H (√3-√6)³

Zapisz w postaci sumy algebraicznej.

A(1-2x)³

B(5x-1)³

C(x-√2)³

D(x+2)² (x²-2x+4)

E(3x-1)² (9x²+3x+1)

F(x²+5x+25)(x-5)²

G(x+2)(x²+4)(x-2)

H(x-1)(x²+x+1)(x³+1)

I(x+2)(x^4+4x²+16)(x-2)

^4 do potegi 4

Answer 1

A (2+√2)³= 8+12√2+12+2√2=20+14√2

B (√5-1)³=5√5-15+3√5-1=-16+8√5=8(√5-2)

C (3-√3)³=9-27√3+27-3√3=35-30√3=5(7-6√3)

D (√2-4)³=2√2-24+48√2-64=-88+50√2=2(-44+25√2)

E (1+2√5)³=1+6√5+60+40√5=46√2+61

F (2√3-3)³=24√3-36+54√3-27=-63+78√3

G (√2+√3)³=2√2+6√3+9√2+3√3=9√3+11√2

H (√3-√6)³=3√3-9√6+18√3-6√6=-15√6+21√3

2.A(1-2x)³=1-6X+12x^2-8x^3=-8x^3+12x^2-6x+1

B(5x-1)³=125x^3-75x^2+15x-1

C(x-√2)³=x^3-3√2x^2+6x-2√2

D(x+2)² (x²-2x+4)=(x^2+4x+4)(x^2-2x+4)=x^4-4x^3+4x^2+4x^3-8x^2+16x+4x^2-8x+16=x^4+8x+16

E(3x-1)² (9x²+3x+1)=(9x^2-6x+1)(9x^2+3x+1)=81x^4+27x^3+9x^2-54x^3-18x^2-6x+9x^2+3x+1=81x^4-27x^3+9x+1

F(x²+5x+25)(x-5)²=(x^2+5x+25)(x^2-10x+25)=x^4-10x^3+25x^2+5x^3-50x^2+75x+25x^2-25x+625=x^4-5x^3+100x+625

G(x+2)(x²+4)(x-2)=(x^3+2x^2+4x+8)(x-2)=x^4+2x^3+4x^2+8x-2x^3-4x^2-8x-16=x^4-16

H(x-1)(x²+x+1)(x³+1)=(x^3+-1)(x^3+1)=x^6-1

I(x+2)(x^4+4x²+16)(x-2)=(x^2-4)(x^4+4x^+16)=x^6+4x^4+16x^2-4x^4-16x^2-64=x^6-64

^4 do potegi 4

^2 do potegi 2 itd