展開する 4(1/2 (x-y))^2+2(x+y)^2

解

展開する

4 (\frac{1}{2} (x - y))^{2} + 2 (x + y)^{2}

4 (\frac{1}{2} (x - y))^{2} + 2 x^{2} + 4 x y + 2 y^{2}

解答ステップ

4 (\frac{1}{2} (x - y))^{2} + 2 (x + y)^{2}

拡張

(x + y)^{2} : x^{2} + 2 x y + y^{2}

= 4 (\frac{1}{2} (x - y))^{2} + 2 (x^{2} + 2 x y + y^{2})

分配法則を適用する:

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

2 (x^{2} + 2 x y + y^{2}) = 2 x^{2} + 2 \cdot 2 x y + 2 y^{2}

= 4 (\frac{1}{2} (x - y))^{2} + 2 x^{2} + 2 \cdot 2 x y + 2 y^{2}

数を乗じる:

2 \cdot 2 = 4

= 4 (\frac{1}{2} (x - y))^{2} + 2 x^{2} + 4 x y + 2 y^{2}