What is expand (r^2cos(θ))(rcos(θ)+rsin(θ)+5) ?

The solution to expand (r^2cos(θ))(rcos(θ)+rsin(θ)+5) is r^3cos^2(θ)+r^3cos(θ)sin(θ)+5r^2cos(θ)

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expand (r^2cos(θ))(rcos(θ)+rsin(θ)+5)

expand

(r^{2} cos (θ)) (r cos (θ) + r sin (θ) + 5)

r^{3} cos^{2} (θ) + r^{3} cos (θ) sin (θ) + 5 r^{2} cos (θ)

Solution steps

(r^{2} cos (θ)) (r cos (θ) + r sin (θ) + 5)

Apply the distributive law:

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

(r^{2} cos (θ)) (r cos (θ) + r sin (θ) + 5) = r^{2} cos (θ) r cos (θ) + r^{2} cos (θ) r sin (θ) + r^{2} cos (θ) \cdot 5

= r^{2} cos (θ) r cos (θ) + r^{2} cos (θ) r sin (θ) + r^{2} cos (θ) \cdot 5

Simplify

r^{2} cos (θ) r cos (θ) + r^{2} cos (θ) r sin (θ) + r^{2} cos (θ) \cdot 5 : r^{3} cos^{2} (θ) + r^{3} cos (θ) sin (θ) + 5 r^{2} cos (θ)

= r^{3} cos^{2} (θ) + r^{3} cos (θ) sin (θ) + 5 r^{2} cos (θ)

8 (16 - π) c m^{2}

- sin (3 x^{2} + 3 x) (6 x + 3)

\frac{5 ( z ^{4} + z ^{3} + z ^{2} + z + 1 )}{z ^{3} ( 5 z - 1 )}

lo g_{10} (3) (x^{2} + 1)

- 6 (3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x))

What is expand (r^2cos(θ))(rcos(θ)+rsin(θ)+5) ?
The solution to expand (r^2cos(θ))(rcos(θ)+rsin(θ)+5) is r^3cos^2(θ)+r^3cos(θ)sin(θ)+5r^2cos(θ)