What is expand (ax^2+bx+c)(dx^2+ex+f) ?

The solution to expand (ax^2+bx+c)(dx^2+ex+f) is adx^4+eax^3+ax^2f+bdx^3+ebx^2+bxf+cdx^2+ecx+cf

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expand (ax^2+bx+c)(dx^2+ex+f)

expand

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

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

Solution steps

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

Distribute parentheses

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

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

Simplify

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

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

(1 - sin (x)) (1 + csc (x)) sin (x)

f (x) = 3 e^{- \frac{x}{5}} (x + 5) + 1

lo g_{10} (2) (x + 1)

\frac{( 6 x ^{2} - 9 x + 1 )}{( x - 1 ) ^{2} ( x + 1 )}

What is expand (ax^2+bx+c)(dx^2+ex+f) ?
The solution to expand (ax^2+bx+c)(dx^2+ex+f) is adx^4+eax^3+ax^2f+bdx^3+ebx^2+bxf+cdx^2+ecx+cf