Question

因式分解(xy+1)^2-(x+y)^2

(xy+1)²-(x+y)²
(x²+2x)²-2(x²+2x)-3
x⁴+4-5x²
已知:a^2+a-6=0.求代数式2a^3+14a^2-60的值

Answer 1

(xy+1)²-(x+y)²=(xy+1-x-y)(xy+1+x+y)
(x²+2x)²-2(x²+2x)-3=(x^2+2x-3)(x^2+2x+1)=(x+3)(x-1)(x+1)^2
x⁴+4-5x²=(x^2-1)(x^2-4).=(x-1)(x+1)(x-2)(x+2)
已知:a^2+a-6=0.
则(a+3)(a-2)=0, 所以a=2或a=-3
当a=2时，
2a^3+14a^2-60＝16+56-60=12
当a=-3时
2a^3+14a^2-60＝－54+126－60＝12
所以2a^3+14a^2-60＝12

Answer 2

(xy+1)^2-(x+y)^2
=(xy+1+(x+y))(xy+1-(x+y))
=(xy+1+x+y)(xy+1-x-y)

(x²+2x)²-2(x²+2x)-3
=(x²+2x-3)(x²+2x+1)
=(x-1)(x+3)(x+1)^2

x⁴+4-5x²
=x⁴-5x²+4
=(x^2-1)(x^2-4)
=(x+1)(x-1)(x+2)(x-2)

已知:a^2+a-6=0
a^2=6-a
代数式2a^3+14a^2-60
=2a(6-a)+14(6-a)-60
=12a-2a^2+84-14a-60
=-2(6-a)+24-2a
=12+2a+24-2a
=36

Answer 3

(xy+1+x+y)(xy+1-x-y)
(x^2+2x-3)(x^2+2x-1)=(x+3)(x-1)(x^2+2x-1)
(x^2-1)(x^-4)=(x+1)(x-1)(x+2)(x-2)

Answer 4

(xy+1)^2-(x+y)^2
=[(xy+1)-(x+y)][(xy+1)+(x+y)]
=(xy+1-x-y)(xy+1+x+y)
=(xy-x+1-y)(xy+x+1+y)
=[x(y-1)-(y-1)][x(y+1)+(y+1)]
=(x-1)(y-1)(y+1)(x+1)

(x²+2x)²-2(x²+2x)-3
=(x²+2x-3)(x²+2x+1)
=(x+3)(x-1)(x+1)²

x⁴+4-5x²
=x⁴-5x²+4
=(x²-4)(x²-1)
=(x+2)(x-2)(x+1)(x-1)

a^2+a-6=0
a^2+a=6
2a^3+14a^2-60
=2a^3+2a^2+12a^2-60
=2a(a^2+a)+12a^2-60
=6*12a+12a^2-60
=12(a^2+a)-60
=12*6-60
=72-60
=12