Question

1. descompuneti in factori folosind formula :a ²- b²=(a+b)·(a-b)
a) a²-4=
b)25-x²=
c)100-x²=
d)36a²-25=
2. calculati folosindformula: a²-b²=(a+b)·(a-b)
a) 17²-13²=
b)153²-53²=
c)123²-23²=
d)26²-25²=
e)51²-49²=
3. restringeti exptesiile urmatoare sub forma: (a±b)²
a) x²+2x+1=
b) 9+6x+x²=
c) 25-10x+x²=
d)36x²+12x+1=
e)x²-2xy+y²=
f) 1+4xy+4x²y²=

Answer 1

1.a)a²-4=(a-2)*(a+2)

b)25-x²=(5-x)*(5+x)

c)100-x²=(10-x)*(10+x)

d)36a²-25=(6a-5)*(6a+5)

2)a)17²-13²=(17-13)*(17+13)=4*30=120

b)153²-53²==(153-53)*(153+53)=100*206=20600

c)123²-23²=(123-23)*(123+23)=100*146=14600

d)26²-25²=(26-23)*(26+23)=1*51=51

e)51²-49²=(51-49)*(51+49)=2*100=200

3.a) x²+2x+1=x²+2*x*1+1²=(x+1)²

b) 9+6x+x²=3²+2*3*x+x²=(3+x)²

c) 25-10x+x²=5²-2*5*x+x²=(5-x)²

d)36x²+12x+1=(6x)²+2*6x*1+1²=(6x+1)²

e)x²-2xy+y²=(x-y)²

f)1+4xy+4x²y²=(1+2xy)²

bafta!