23)
a) (x-√7)(x+√7)-(x+1)²= x²-7-x²-2x-1=-8-2x=-2(4-x)
b) (√5x+3)²-(2√5x-√3)(2√5x+√3)+(3√5x-1)²=
= 5x²+6√5+9-20x²+3+45x²-6√5x+1= 30x²+13
c) (2x-√3)²+(2√3x+1)²-(3√3x-√7)(3√5x+√7)=
= 4x²-4√3x+3+12x²+4√3x+1-27x²+7= 11-11x²=11(1-x²)=11(1-x)(1+x)
d) (√3x-2)²+(2√3+x)²+(√5x-4)(√5x+4)= 3x²-4√3x+4+12+4√3x+x²+5x²-16=
= 9x²
e) (3x-√2)²+(√6+√3x)²-(√15-√2x)(√15+2x)= =9x²-6√2x+2+6+2√18x+3x²-15+2x²=
=14x²-6√2x+8+6√2x-15=14x²-7=7(2x²-1)=2(√2x-1)(√2x+1)
f)(a-√3)(a+√3)+(a-√5)(a+√5)-(a-√7)(a+√7)=a²-3+a²-5-a²+7= 2a²-1=
=(√2a-1)(√2a+1)
