Question

1 Zapisz w postaci sumy algebraicznej : (wzory skróconego mnożenia)

a) (2√3 -5) (2√3 + 5)

b) (√7 - 3√2)²

c) ( 2√5 +3√2)³

d) (3x+5y)²

e) (3y -6x)³

Answer 1

[2√3-5][2√3+5]=[2√3]²-5²=12-25=-13

[√7-3√2]²=√7²-2√7×3√2+[3√2]²=7-6√14+18=25-6√14

[2√5+3√2]³=40√5+180√2+108√5+54√2=148√5+234√2

[3x+5y]²=9x²+30xy+25y²

[3y-6x]³=27y³-162xy²+324x²y-216x³

Answer 2

a) (2√3 -5) (2√3 + 5)=(2√3)²-5²

b) (√7 - 3√2)²= (√7)²-2* 7*3√2+(3√2)²

c) ( 2√5 +3√2)³=(2√5)³+3*2√5*3√2+3*2√5*3√2+(3√2)³

d)  (3x+5y)²=3x²+2*3x*5y+5y²

e) (3y -6x)³=3y-3*3y*6x+3*3y*6x-6x³