What is factor 9-12cos(4x)+4cos^2(4x) ?

The solution to factor 9-12cos(4x)+4cos^2(4x) is (2cos(4x)-3)^2

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factor 9-12cos(4x)+4cos^2(4x)

factor

9 - 12 cos (4 x) + 4 cos^{2} (4 x)

(2 cos (4 x) - 3)^{2}

Solution steps

9 - 12 cos (4 x) + 4 cos^{2} (4 x)

Write in the standard form

a x^{2} + b x + c

= 4 cos^{2} (4 x) - 12 cos (4 x) + 9

Rewrite

4 cos^{2} (4 x) - 12 cos (4 x) + 9

(2 cos (4 x))^{2} - 2 \cdot 2 cos (4 x) \cdot 3 + 3^{2}

= (2 cos (4 x))^{2} - 2 \cdot 2 cos (4 x) \cdot 3 + 3^{2}

Apply Perfect Square Formula:

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

a = 2 cos (4 x), b = 3

= (2 cos (4 x) - 3)^{2}

18 x^{4} + 2 1^{2} + 5

\frac{2 a - 2 b}{5 a - 5 b}

x (x + 2) + x (x + 2)

2 (x sin (x))

15 - 4^{'} 9

What is factor 9-12cos(4x)+4cos^2(4x) ?
The solution to factor 9-12cos(4x)+4cos^2(4x) is (2cos(4x)-3)^2