Question

1. Descompuneti in factori:
a) 3x²-6x
b) x³+x²y-xy²-y³
c) 4x²-81y²
d) 16x la puterea 4 - 25y la puterea 4.
e) 4x²-12xy+9y²
f) 25x²+10x+1
g) x²+6x+8
h) x²-2x-3
i) x la puterea 4-13x²+36
j) (x²+y²)²-4x²y²
2. Arata ca (√3+√7-√11)(√3+√7+√11)+(√3-√7)² este numar rational.
VA ROG MULT. DAU COROANA

Answer 1

a) 3x²-6x=3x(x-2)
b) x³+x²y-xy²-y³=x²(x+y)-y²(x+y)=(x+y)(x²-y²)
c) 4x²-81y²=(2x-9y)(2x+9y)
d) 16x^4 - 25y^4=(4x^2-5y^2)(4x^2+5y^2)
e) 4x²-12xy+9y²=(2x-3y)²
f) 25x²+10x+1=25x²+5x+5x+1=5x(5x+1)+1(5x+1)=(5x+1)(5x+1)=(5x+1)²
g) x²+6x+8=x²+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)
h) x²-2x-3=x²-3x+x-3=x(x-3)+1(x-3)=(x-3)(x+1)
i) x^4-13x²+36=x^4-4x^2-9x^2+36=x²(x²-4)-9(x²-4)=(x²-4)(x²-9)
j) (x²+y²)²-4x²y²=x^4 +2x^2y^2+y^4-4x^2y^2=
x^4 -2x^2y^2+y^4=x^4-x^2y^2-x^2y^2+y^4=x²(x²-y²)-y²(x²-y²)=(x²-y²)(x²-y²)
=(x²-y²)²
2. (√3+√7-√11)(√3+√7+√11)+(√3-√7)²
3+√3√7+√3√11+√3√7+7+√7√11-√3√11-√7√11-11+ 3-2√3√7+7=
=10+2√3√7-11+ 3-2√3√7+7=
=9