Question

DAU COROANA
Descompuneti in factori :
a) (2x+5)^2-(x+3)^2
b) (3x+4)^2-(x+5)^2
c) (2x+1)^2-(x-1)^2
d) (3x+2)^2-(2x+1)^2
e) (3x-1)^2-4(x+1)^2
f) (4x-3)^2-9(x+2)^2

Answer 1

la toate aplici formula cu (a+b)^2=a^2+2ab+b^2 sau la cele cu - in paranteza este formula: (a-b)^2=a^2-2ab+b^2. 

Answer 2

a)  (2x+5)²-(x+3)²=(4x²+2·2x·5+5²)-(x²+2·x·3+3²)=4x²-x²+20x+25-x²+6x+9=4x²-x²+20x-6x+25-9=3x²+14-16    b)    (3x+4)²-(x+5)²=(9x²+2·3x·4+4²)-(x²+2·x·5+5²)=9x²+24x+16-x²+10x+25=9x²-x²+8x-24x+16-25=8x²-16x-9   c)  (2x+1)²-(x-1)²=4x²+2·2x·1)-(x²+2·x·(-1)-1²=4x²-x²+4x-2x+1-1=3x²-2x    d)  (3x+2)²-(2x+1)²=(9x²+2·3x·2+2²)-(4x²+2·2x·1+1²)=9x²+12x+4-x²+4x+1=9x²-x²+12x-4x+4-1=8x²-8x+5  e)  (3x+1)²-4(x+1)²=(9x²+2·3x·1+1²)-(4x+4)²=(9x²+6x+1)-(16x²+2·4x·4+4²)=9x²+6x+1-16x²+32x+16=9x²-16x²+6x+32x-1+16 =-7x²+38x-17   f)   (4x-3)²-9(x+2)²=(16x²-2·4x·3-3²)-(9x+18)²=16x²-24x-9-81x²+2·9x·18+18²=16x²-24x-9-81x²-324x+324=16x²-81x²+24x-324x-9+324=65x²-300x-315