把下列各式分解因式:①(m-n)^2010-16(m-n)^2011
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把下列各式分解因式:①(m-n)^2010-16(m-n)^2011
:①(m-n)^2010-16(m-n)^2011
②1/2x^2-8ax+32a^2;
③5a^2b(x-y)^3-30ab^2(y-x)^2
④a^2-(b^2+c^2-2ac)
⑤x^2(x^2-y^2)+z^2(y^2-x^2)
⑥(a+2)(a+4)+1
⑦(a+b)^2+4(a+b+1)
:①(m-n)^2010-16(m-n)^2011
②1/2x^2-8ax+32a^2;
③5a^2b(x-y)^3-30ab^2(y-x)^2
④a^2-(b^2+c^2-2ac)
⑤x^2(x^2-y^2)+z^2(y^2-x^2)
⑥(a+2)(a+4)+1
⑦(a+b)^2+4(a+b+1)
![把下列各式分解因式:①(m-n)^2010-16(m-n)^2011](/uploads/image/z/19353555-27-5.jpg?t=%E6%8A%8A%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%EF%BC%9A%E2%91%A0%EF%BC%88m-n%EF%BC%89%5E2010-16%EF%BC%88m-n%EF%BC%89%5E2011)
①(m-n)^2010-16(m-n)^2011
=(m-n)^2010-16(m-n)^2010*(m-n)
=(m-n)^2010[1-16(m-n)]
=(1-16m+16n)(m-n)^2010
②1/2x^2-8ax+32a^2;
=1/2(x^2-16ax+64a^2)
=1/2(x-8a)^2
③5a^2b(x-y)^3-30ab^2(y-x)^2
=5a^2b(x-y)^3-30ab^2(x-y)^2
=5ab(x-y)^2[a(x-y)-6b]
=5ab(x-y)^2(ax-ay-6b)
④a^2-(b^2-c^2-2ac)
=a^2-b^2+c^2+2ac
=a^2+c^2+2ac-b^2
=(a+c)^2-b^2
=(a+c+b)(a+c-b)
⑤x^2(x^2-y^2)+z^2(y^2-x^2)
=x^2(x^2-y^2)-z^2(x^2-y^2)
=(x^2-z^2)(x^2-y^2)
=(x-z)x+z)(x-y)(x+y)
⑥(a+2)(a+4)+1
=a^2+6a+8+1
=a^2+6a+9
=(a+3)^2
⑦(a+b)^2+4(a+b+1)
=(a+b)^2+4(a+b)+4
=(a+b+2)^2
=(m-n)^2010-16(m-n)^2010*(m-n)
=(m-n)^2010[1-16(m-n)]
=(1-16m+16n)(m-n)^2010
②1/2x^2-8ax+32a^2;
=1/2(x^2-16ax+64a^2)
=1/2(x-8a)^2
③5a^2b(x-y)^3-30ab^2(y-x)^2
=5a^2b(x-y)^3-30ab^2(x-y)^2
=5ab(x-y)^2[a(x-y)-6b]
=5ab(x-y)^2(ax-ay-6b)
④a^2-(b^2-c^2-2ac)
=a^2-b^2+c^2+2ac
=a^2+c^2+2ac-b^2
=(a+c)^2-b^2
=(a+c+b)(a+c-b)
⑤x^2(x^2-y^2)+z^2(y^2-x^2)
=x^2(x^2-y^2)-z^2(x^2-y^2)
=(x^2-z^2)(x^2-y^2)
=(x-z)x+z)(x-y)(x+y)
⑥(a+2)(a+4)+1
=a^2+6a+8+1
=a^2+6a+9
=(a+3)^2
⑦(a+b)^2+4(a+b+1)
=(a+b)^2+4(a+b)+4
=(a+b+2)^2
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