Question

Descompuneti in factori:
a)(x+√3)²-(2√3)³;
b)(y-√2)²-(2√2)²;
c)(√3x-1)²-3;
d)(2x+√5)²-45;
e)27x²-(1-√3x)²;
f)(x+√2y)²-8y²;
g)(x+√3)²-(2x+2√3);
h)8x²-(√2x+1)²;
i)(3x/5-y)²-4y².
J)(2x+1/4)²-(x-3/4)²;
k)(x+√3)²-(2√3)

Va rog frumos sa ma ajutati si pe mine la rezolvare!

Answer 1

a)(x+√3)²-(2√3)²=(x+√3-2√3)(x+√3+2√3)=(x-√3)(x+3√3)
b)(y-√2)²-(2√2)²=(y-√2-2√2)(y-√2+2√2)=(y-3√2)(y+√2)
c)(√3x-1)²-3=(√3x-1-√3)(√3x-1+√3)
d)(2x+√5)²-45=(2x+√5-3√5)(2x+√5+3√5)=(2x-2√5)(2x+4√5)
e)27x²-(1-√3x)²=3√3x-1+√3x)(3√3x+1-√3x)=(4√3x-1)(2√3x+1)
f)(x+√2y)²-8y²=(x+√2y-2√2y)(x+√2y+2√2y)=(x-√2y)(x+3√2y)
g)(x+√3)²-(2x+2√3)²=(x+√3-2x-2√3)(x+√3+2x+2√3)=(-x-√3)(3x+3√3)
h)8x²-(√2x+1)²=(2√2x-√2x-1)(2√2x+√2x+1)=(√2x-1)(3√2x+1)
i)(3x/5-y)²-4y²=(3x/5-y-2y)(3x/5-y+2y)=(3x/5-3y)(3x/5+y)
J)(2x+1/4)²-(x-3/4)²=(2x+1/4-x+3/4)(2x+1/4+x-3/4)=(x+1)(3x-1/2)
k)(x+√3)²-(2√3)²=(x+√3-2√3)(x+√3+2√3)=(x-√3)(x+3√3)