What is expand (a+bt)^3 ?

The solution to expand (a+bt)^3 is a^3+3a^2bt+3ab^2t^2+b^3t^3

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expand (a+bt)^3

expand

(a + b t)^{3}

a^{3} + 3 a^{2} b t + 3 a b^{2} t^{2} + b^{3} t^{3}

Solution steps

(a + b t)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(a + b t)^{3} = a^{3} + 3 a^{2} b t + 3 a (b t)^{2} + (b t)^{3}

= a^{3} + 3 a^{2} b t + 3 a (b t)^{2} + (b t)^{3}

Simplify

a^{3} + 3 a^{2} b t + 3 a (b t)^{2} + (b t)^{3} : a^{3} + 3 a^{2} b t + 3 a b^{2} t^{2} + b^{3} t^{3}

= a^{3} + 3 a^{2} b t + 3 a b^{2} t^{2} + b^{3} t^{3}

i - 0.3 i

x^{2} + 5 x^{2}

9 x^{2} + 9 x^{2}

(- 2 - 2 i) (- 2 + 2 i)

e^{5 i}

What is expand (a+bt)^3 ?
The solution to expand (a+bt)^3 is a^3+3a^2bt+3ab^2t^2+b^3t^3