What is expand (a+bx+cx^2)(d+ex+fx^2) ?

The solution to expand (a+bx+cx^2)(d+ex+fx^2) is ad+eax+ax^2f+bdx+ebx^2+bx^3f+cdx^2+ecx^3+cx^4f

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expand (a+bx+cx^2)(d+ex+fx^2)

expand

(a + b x + c x^{2}) (d + e x + f x^{2})

a d + e a x + a x^{2} f + b d x + e b x^{2} + b x^{3} f + c d x^{2} + ec x^{3} + c x^{4} f

Solution steps

(a + b x + c x^{2}) (d + e x + f x^{2})

= (a + b x + c x^{2}) (d + e x + x^{2} f)

Distribute parentheses

= a d + a e x + a f x^{2} + b x d + b x e x + b x f x^{2} + c x^{2} d + c x^{2} e x + c x^{2} f x^{2}

= a d + e a x + a x^{2} f + b d x + e b xx + b x^{2} x f + c d x^{2} + ec x^{2} x + c x^{2} x^{2} f

Simplify

a d + e a x + a x^{2} f + b d x + e b xx + b x^{2} x f + c d x^{2} + ec x^{2} x + c x^{2} x^{2} f : a d + e a x + a x^{2} f + b d x + e b x^{2} + b x^{3} f + c d x^{2} + ec x^{3} + c x^{4} f

= a d + e a x + a x^{2} f + b d x + e b x^{2} + b x^{3} f + c d x^{2} + ec x^{3} + c x^{4} f

sec (x) (csc (x) - 1) + cos (x) (sec^{2} (x) - csc (x))

(23 - 2 i)^{8}

\frac{x + 1}{x ^{\frac{2}{3}} ( x + 3 ) ^{\frac{1}{3}}}

\frac{2 ( x ^{4} - 1 )}{x ^{3}}

(2 - e^{- x})^{2}

What is expand (a+bx+cx^2)(d+ex+fx^2) ?
The solution to expand (a+bx+cx^2)(d+ex+fx^2) is ad+eax+ax^2f+bdx+ebx^2+bx^3f+cdx^2+ecx^3+cx^4f