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Factorise:a4+2a3b-2ab3-b4..

Sagot :

[tex]a^4+2a^3b-2ab^3-b^4\\\\=a^4-b^4+2a^3b-2ab^3\\\\=(a^2-b^2)(a^2+b^2)+2ab(a^2-b^2)\\\\=(a^2-b^2)(a^2+b^2+2ab)\\\\=(a-b)(a+b)(a+b)^2\\\\=(a-b)(a+b)(a+b)(a+b)[/tex]


[tex](x+y)^2=x^2+2xy+y^2\\\\x^2-y^2=(x-y)(x+y)[/tex]