What is expand (a+b*cos(t))^3 ?

The solution to expand (a+b*cos(t))^3 is a^3+3a^2bcos(t)+3ab^2cos^2(t)+b^3cos^3(t)

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expand (a+b*cos(t))^3

expand

(a + b \cdot cos (t))^{3}

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

Solution steps

(a + b cos (t))^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

95 (1 + 3)

(x + y = 1, 2) (x - 2 y = 16)

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

(2 5 - 3) \cdot (25 - 7)

(1 + 0.003 e^{0.8 t})^{2}

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