大师作文网(1)ab(x+y)(x-y)-xy(a+b)(a-b) (2)x^4+x^2-2ax+1-a^2 (3)a^4-a^2
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(1)ab(x+y)(x-y)-xy(a+b)(a-b) (2)x^4+x^2-2ax+1-a^2 (3)a^4-a^2+4a-4
ab(x+y)(x-y)-xy(a+b)(a-b)
=ab(x^2-y^2)-xy(a^2-b^2)
=abx^2-aby^2-xya^2+xyb^2
=ax(bx-ay)-by(ay-bx)
=ax(bx-ay)+by(bx-ay)
=(ax+by)(bx-ay)
x^4+x^2-2ax+1-a^2
=x^4+2x^2+1-(x^2-2ax+a^2)
=(x^2+1)^2-(x-a)^2
=(x^2+1+x-a)(x^2+1-x+a)
a^4-a^2+4a-4
=a^4-(a^2-4a+4)
=a^4-(a-2)^2
=(a^2+a-2)(a^2-a+2)
=(a+2)(a-1)(a^2-a+2)
=ab(x^2-y^2)-xy(a^2-b^2)
=abx^2-aby^2-xya^2+xyb^2
=ax(bx-ay)-by(ay-bx)
=ax(bx-ay)+by(bx-ay)
=(ax+by)(bx-ay)
x^4+x^2-2ax+1-a^2
=x^4+2x^2+1-(x^2-2ax+a^2)
=(x^2+1)^2-(x-a)^2
=(x^2+1+x-a)(x^2+1-x+a)
a^4-a^2+4a-4
=a^4-(a^2-4a+4)
=a^4-(a-2)^2
=(a^2+a-2)(a^2-a+2)
=(a+2)(a-1)(a^2-a+2)
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