What is expand 4(1+cos(3x^2))^4 ?

The solution to expand 4(1+cos(3x^2))^4 is 4+16cos(3x^2)+24cos^2(3x^2)+16cos^3(3x^2)+4cos^4(3x^2)

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expand 4(1+cos(3x^2))^4

expand

4 (1 + cos (3 x^{2}))^{4}

4 + 16 cos (3 x^{2}) + 24 cos^{2} (3 x^{2}) + 16 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

Solution steps

4 (1 + cos (3 x^{2}))^{4}

Expand

(1 + cos (3 x^{2}))^{4} : 1 + 4 cos (3 x^{2}) + 6 cos^{2} (3 x^{2}) + 4 cos^{3} (3 x^{2}) + cos^{4} (3 x^{2})

= 4 (1 + 4 cos (3 x^{2}) + 6 cos^{2} (3 x^{2}) + 4 cos^{3} (3 x^{2}) + cos^{4} (3 x^{2}))

Distribute parentheses

= 4 \cdot 1 + 4 \cdot 4 cos (3 x^{2}) + 4 \cdot 6 cos^{2} (3 x^{2}) + 4 \cdot 4 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

Simplify

4 \cdot 1 + 4 \cdot 4 cos (3 x^{2}) + 4 \cdot 6 cos^{2} (3 x^{2}) + 4 \cdot 4 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2}) : 4 + 16 cos (3 x^{2}) + 24 cos^{2} (3 x^{2}) + 16 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

= 4 + 16 cos (3 x^{2}) + 24 cos^{2} (3 x^{2}) + 16 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

(x - 3) (x^{2} + 5)

\frac{1}{( 3 x + 1 ) ^{2}}

\frac{d x}{( x + 2 ) ( x ^{2} + 2 x + 4 ) ^{2}}

- \frac{1}{( x - 5 ) ^{2}}

- \frac{1.2 ( 1 - 0.03 x ^{2} )}{( 0.01 x ^{2} + 1 ) ^{3}}

What is expand 4(1+cos(3x^2))^4 ?
The solution to expand 4(1+cos(3x^2))^4 is 4+16cos(3x^2)+24cos^2(3x^2)+16cos^3(3x^2)+4cos^4(3x^2)