What is expand (-5-5cos(θ))^2*1/2 ?

The solution to expand (-5-5cos(θ))^2*1/2 is (25+25cos^2(θ))/2+25cos(θ)

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expand (-5-5cos(θ))^2*1/2

expand

(- 5 - 5 cos (θ))^{2} \cdot \frac{1}{2}

\frac{25 + 25 cos ^{2} ( θ )}{2} + 25 cos (θ)

Solution steps

(- 5 - 5 cos (θ))^{2} \frac{1}{2}

= \frac{1}{2} (- 5 - 5 cos (θ))^{2}

Expand

(- 5 - 5 cos (θ))^{2} : 25 + 50 cos (θ) + 25 cos^{2} (θ)

= \frac{1}{2} (25 + 50 cos (θ) + 25 cos^{2} (θ))

Apply the distributive law:

m (a + b + c) = ma + mb + m c

\frac{1}{2} (25 + 50 cos (θ) + 25 cos^{2} (θ)) = \frac{1}{2} \cdot 25 + \frac{1}{2} \cdot 50 cos (θ) + \frac{1}{2} \cdot 25 cos^{2} (θ)

= \frac{1}{2} \cdot 25 + \frac{1}{2} \cdot 50 cos (θ) + \frac{1}{2} \cdot 25 cos^{2} (θ)

Simplify

\frac{1}{2} \cdot 25 + \frac{1}{2} \cdot 50 cos (θ) + \frac{1}{2} \cdot 25 cos^{2} (θ) : \frac{25 + 25 cos ^{2} ( θ )}{2} + 25 cos (θ)

= \frac{25 + 25 cos ^{2} ( θ )}{2} + 25 cos (θ)

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What is expand (-5-5cos(θ))^2*1/2 ?
The solution to expand (-5-5cos(θ))^2*1/2 is (25+25cos^2(θ))/2+25cos(θ)