What is expand (5e^3+4t^2)^2 ?

The solution to expand (5e^3+4t^2)^2 is 16t^4+40e^3t^2+25e^6

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expand (5e^3+4t^2)^2

expand

(5 e^{3} + 4 t^{2})^{2}

16 t^{4} + 40 e^{3} t^{2} + 25 e^{6}

Solution steps

(5 e^{3} + 4 t^{2})^{2}

Apply Perfect Square Formula:

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

a = 5 e^{3}, b = 4 t^{2}

= (5 e^{3})^{2} + 2 \cdot 5 e^{3} \cdot 4 t^{2} + (4 t^{2})^{2}

Simplify

(5 e^{3})^{2} + 2 \cdot 5 e^{3} \cdot 4 t^{2} + (4 t^{2})^{2} : 25 e^{6} + 40 e^{3} t^{2} + 16 t^{4}

= 25 e^{6} + 40 e^{3} t^{2} + 16 t^{4}

Rewrite in standard form

= 16 t^{4} + 40 e^{3} t^{2} + 25 e^{6}

[(2 x - 3) (2 x + 3)]^{2}

(3 x^{2} + 6 x + 1)^{5}

5 x^{3} y (6 x y^{5})

\frac{( 3 x - y ) ^{2}}{81}

\frac{x ^{3}}{2 ( x ^{2} - 4 )}

What is expand (5e^3+4t^2)^2 ?
The solution to expand (5e^3+4t^2)^2 is 16t^4+40e^3t^2+25e^6