What is expand (2u^2cos(v)+1)^2 ?

The solution to expand (2u^2cos(v)+1)^2 is 4u^4cos^2(v)+4u^2cos(v)+1

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expand (2u^2cos(v)+1)^2

expand

(2 u^{2} cos (v) + 1)^{2}

4 u^{4} cos^{2} (v) + 4 u^{2} cos (v) + 1

Solution steps

(2 u^{2} cos (v) + 1)^{2}

Apply Perfect Square Formula:

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

(2 u^{2} cos (v) + 1)^{2} = (2 u^{2} cos (v))^{2} + 2 \cdot 2 u^{2} cos (v) \cdot 1 + 1^{2}

= (2 u^{2} cos (v))^{2} + 2 \cdot 2 u^{2} cos (v) \cdot 1 + 1^{2}

Simplify

(2 u^{2} cos (v))^{2} + 2 \cdot 2 u^{2} cos (v) \cdot 1 + 1^{2} : 4 u^{4} cos^{2} (v) + 4 u^{2} cos (v) + 1

= 4 u^{4} cos^{2} (v) + 4 u^{2} cos (v) + 1

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(sin (6 x) - cos (6 x))^{2}

What is expand (2u^2cos(v)+1)^2 ?
The solution to expand (2u^2cos(v)+1)^2 is 4u^4cos^2(v)+4u^2cos(v)+1