What is expand (t^2+bt+c)(t^2+dt+e) ?

The solution to expand (t^2+bt+c)(t^2+dt+e) is t^4+t^2dt+et^2+t^3b+tbdt+etb+ct^2+cdt+ec

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expand (t^2+bt+c)(t^2+dt+e)

expand

(t^{2} + b t + c) (t^{2} + d t + e)

t^{4} + t^{2} d t + e t^{2} + t^{3} b + t b d t + e t b + c t^{2} + c d t + ec

Solution steps

(t^{2} + b t + c) (t^{2} + d t + e)

= (t^{2} + t b + c) (t^{2} + d t + e)

Distribute parentheses

= t^{2} t^{2} + t^{2} d t + t^{2} e + b t t^{2} + b t d t + b t e + c t^{2} + c d t + ce

= t^{2} t^{2} + t^{2} d t + e t^{2} + t^{2} t b + t b d t + e t b + c t^{2} + c d t + ec

Simplify

t^{2} t^{2} + t^{2} d t + e t^{2} + t^{2} t b + t b d t + e t b + c t^{2} + c d t + ec : t^{4} + t^{2} d t + e t^{2} + t^{3} b + t b d t + e t b + c t^{2} + c d t + ec

= t^{4} + t^{2} d t + e t^{2} + t^{3} b + t b d t + e t b + c t^{2} + c d t + ec

\frac{200}{s ( s ^{3} + 6 s ^{2} + 11 s + 6 )}

\frac{s + 10}{( s + 2 ) ( s ^{2} + 6 s + 25 )}

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

5 (3 - 2)

\frac{( z ^{2} + 1 ) ^{2}}{( z - i ) ^{2}}

What is expand (t^2+bt+c)(t^2+dt+e) ?
The solution to expand (t^2+bt+c)(t^2+dt+e) is t^4+t^2dt+et^2+t^3b+tbdt+etb+ct^2+cdt+ec