展開する (9cos(t)sin(t)+9cos^2(t))^2

解

展開する

(9 cos (t) sin (t) + 9 cos^{2} (t))^{2}

81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t)

解答ステップ

(9 cos (t) sin (t) + 9 cos^{2} (t))^{2}

完全平方式を適用する:

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

(9 cos (t) sin (t) + 9 cos^{2} (t))^{2} = (9 cos (t) sin (t))^{2} + 2 \cdot 9 cos (t) sin (t) \cdot 9 cos^{2} (t) + (9 cos^{2} (t))^{2}

= (9 cos (t) sin (t))^{2} + 2 \cdot 9 cos (t) sin (t) \cdot 9 cos^{2} (t) + (9 cos^{2} (t))^{2}

簡素化

(9 cos (t) sin (t))^{2} + 2 \cdot 9 cos (t) sin (t) \cdot 9 cos^{2} (t) + (9 cos^{2} (t))^{2} : 81 cos^{2} (t) (sin (2 t) + 1)

= 81 cos^{2} (t) (sin (2 t) + 1)

分配法則を適用する:

a (b + c) = ab + a c

81 cos^{2} (t) (sin (2 t) + 1) = 81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t) \cdot 1

= 81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t) \cdot 1

数を乗じる:

81 \cdot 1 = 81

= 81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t)