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 + \frac{x}{2})^{10}

(2 - i)^{5}

2 (1 + cos (θ))

\frac{4 ab}{( a + b ) ^{2}}

2 y d x + (3 y - 2 x) d y

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