What is expand (5x^3zb+7d^5e^7)^2 ?

The solution to expand (5x^3zb+7d^5e^7)^2 is 25b^2x^6z^2+70e^7bd^5x^3z+49e^{14}d^{10}

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expand (5x^3zb+7d^5e^7)^2

expand

(5 x^{3} z b + 7 d^{5} e^{7})^{2}

25 b^{2} x^{6} z^{2} + 70 e^{7} b d^{5} x^{3} z + 49 e^{14} d^{10}

Solution steps

(5 x^{3} z b + 7 d^{5} e^{7})^{2}

= (5 b x^{3} z + 7 e^{7} d^{5})^{2}

Apply Perfect Square Formula:

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

a = 5 x^{3} z b, b = 7 d^{5} e^{7}

= (5 x^{3} z b)^{2} + 2 \cdot 5 x^{3} z b \cdot 7 d^{5} e^{7} + (7 d^{5} e^{7})^{2}

Simplify

(5 x^{3} z b)^{2} + 2 \cdot 5 x^{3} z b \cdot 7 d^{5} e^{7} + (7 d^{5} e^{7})^{2} : 25 b^{2} x^{6} z^{2} + 70 e^{7} b d^{5} x^{3} z + 49 e^{14} d^{10}

= 25 b^{2} x^{6} z^{2} + 70 e^{7} b d^{5} x^{3} z + 49 e^{14} d^{10}

\frac{1}{n ( n + 2 )}

3 (3 x^{2} + y^{2}) d x - 2 x y d y

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

(\frac{x ^{2}}{2} + x) x e^{2 x}

\frac{d}{d x} ((x^{2} - a) e^{x}) + b x

What is expand (5x^3zb+7d^5e^7)^2 ?
The solution to expand (5x^3zb+7d^5e^7)^2 is 25b^2x^6z^2+70e^7bd^5x^3z+49e^{14}d^{10}