在实数范围内分解因式-3xy^2-6x^y,(x+y)^2-4xy,(a+b)^2-16(a-b)^2
⑴-3xy^2-6x^y,⑵(x+y)^2-4xy,⑶(a+b)^2-16(a-b)^2,⑷a^4-4a^2b^2+4b^4,⑸2x^2-7x+3...
⑴-3xy^2-6x^y,⑵(x+y)^2-4xy,⑶(a+b)^2-16(a-b)^2,⑷a^4-4a^2b^2+4b^4,⑸2x^2-7x+3
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2011-01-31
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⑴-3xy^2-6x^2y
=-3xy(x+2y)
⑵(x+y)^2-4xy
=x^2+2xy+y^2-4xy
=x^2-2xy+y^2
=(x-y)^2
⑶(a+b)^2-16(a-b)^2
=(a+b)^2-(4a-4b)^2
=(a+b+4a-4b)(a+b-4a+4b)
=(5a-3b)(5b-3a)
⑷a^4-4a^2b^2+4b^4
=(a^2-2b^2)^2
⑸2x^2-7x+3
=2x^2-x-6x+3
=x(2x-1)-3(2x-1)
=(2x-1)(x-3)
=-3xy(x+2y)
⑵(x+y)^2-4xy
=x^2+2xy+y^2-4xy
=x^2-2xy+y^2
=(x-y)^2
⑶(a+b)^2-16(a-b)^2
=(a+b)^2-(4a-4b)^2
=(a+b+4a-4b)(a+b-4a+4b)
=(5a-3b)(5b-3a)
⑷a^4-4a^2b^2+4b^4
=(a^2-2b^2)^2
⑸2x^2-7x+3
=2x^2-x-6x+3
=x(2x-1)-3(2x-1)
=(2x-1)(x-3)
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