Question

solve this middle term: x^3+6x^2y+11xy^2+ 6y^3​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

f(x)=x^3–6x^2y+11xy^2–6y^3.

put x=y , f(y)= y^3–6y^3+11y^3–6y^3 =0,

Therefore (x-y) is a factor of f(x).

x^3–6x^2y+11xy^2–6y^3.

=x^2(x-y)+x^2y-6x^2y+11xy^2–6y^3.

=x^2(x-y)-5x^2y+11xy^2–6y^3.

=x^2(x-y)-5xy(x-y)-5xy^2+11xy^2–6y^3.

=x^2(x-y)-5xy(x-y)+6xy^2–6y^3.

=x^2(x-y)-5xy(x-y)+6y^2(x-y).

= (x-y)[x^2–5xy+6y^2].

=(x-y)[x^2–2xy-3xy+6y^2].

=(x-y)[x(x-2y)-3y(x-2y)].

=(x-y) (x-2y) (x-3y) . Proved.