(x^2+y^2)(x^2+y^2—8)+16分解因式=?请写下具体过程
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(x^2+y^2)(x^2+y^2—8)+16分解因式=?请写下具体过程
(x^2+y^2)(x^2+y^2—8)+16分解因式=?
请写下具体过程
(x^2+y^2)(x^2+y^2—8)+16分解因式=?请写下具体过程
令x^2+y^2=t
则:原式=t(t-8)+16
=t^2-8t+16
=(t-4)^2
=(x^2+y^2-4)^2
(x^2+y^2)(x^2+y^2—8)+16
设x^2+y^2=k
k(k-8)+16
=k^2-8k+16
=(k-4)^2
把x^2+y^2=k代入
=(x^2+y^2-4)^2
(x^2+y^2-4)^2
(x^2+y^2)(x^2+y^2—8)+16
令a=x^2+y^2
a(a-8)+16
a^2-8a+16
(a-4)^2
(x^2+y^2-4)^2
(x^2+y^2)(x^2+y^2—8)+16
=(x^+y^2)^2-8(x^y+y^2)+16
=(x^2+y^2)^2-2*4*(x^2+y^2)+4^2
=(x^2+y^2-4)^2
设k=x^2+y^2
式子为:k*(k-8)+16=>
k^2-8k+16=>
(k-4)^2
把k=x^2+y^2带入得
(x^2+y^2-4)^2
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