Question

Descompuneti in factori,aplicand formula a²-b²=(a+b)(a-b) :
a) (x-√3)²-(2√3)²
b) (√2-y)²-(√2)²
c) (√3x-1)²-3
d) (2x+√5)²-√45
e) 27x²-(1-√3x)²
f) (a+√2b)²-8b²
g) (x+√7)²-(2x+2√7)²
h)8x²-(√2x+1)²
i) (x+√3)⁴-(√3)⁴

Answer 1

a)(x-√3)²-(2√3)²⇒(x²-2√3x+3)-36⇒x²-2√3x-33
b)(√2-y)²-(√2)²=2-2√2y+y²-2⇒-2√2y+y²
c)(√3x-1)²-3⇒3x²-2√3x+1-3⇒3x²-2√3x-2
d)(2x+√5)²-√45⇒4x²-2√5x+5-√45⇒4x²-2√5x+5-3√5
e)27x²-(1-√3x)²=⇒27x²-(1-2√3x+3x)⇒27x²-1+2√3x+3x
f)(a-√2b)²-8b²⇒a²-2√2ab+2b²-8b²=⇒a²-2√2-6b²
g)(x+√7)²-(2x+2√7)²⇒(x²+2√7x+7)-(4x²+8√7x+14)⇒
h)8x²-(√2x+1)²=8x²-(2x²+2√2x+1)⇒8x²-2x²-2√2x-1⇒6x²-2√2x-1
i)(x+√3)⁴-(√3)⁴⇒x⁴+9-9⇒x⁴
sucees