What is expand (ce^{t^2}+4t)^2 ?

The solution to expand (ce^{t^2}+4t)^2 is c^2e^{2t^2}+8ce^{t^2}t+16t^2

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expand (ce^{t^2}+4t)^2

expand

(c e^{t^{2}} + 4 t)^{2}

c^{2} e^{2 t^{2}} + 8 c e^{t^{2}} t + 16 t^{2}

Solution steps

(c e^{t^{2}} + 4 t)^{2}

Apply Perfect Square Formula:

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

a = c e^{t^{2}}, b = 4 t

= (c e^{t^{2}})^{2} + 2 c e^{t^{2}} \cdot 4 t + (4 t)^{2}

Simplify

(c e^{t^{2}})^{2} + 2 c e^{t^{2}} \cdot 4 t + (4 t)^{2} : c^{2} e^{2 t^{2}} + 8 c e^{t^{2}} t + 16 t^{2}

= c^{2} e^{2 t^{2}} + 8 c e^{t^{2}} t + 16 t^{2}

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What is expand (ce^{t^2}+4t)^2 ?
The solution to expand (ce^{t^2}+4t)^2 is c^2e^{2t^2}+8ce^{t^2}t+16t^2