展开 (3x-sqrt(5y^2-3x+19)+5)^2

解答

展开

(3 x - 5 y^{2} - 3 x + 19 + 5)^{2}

9 x^{2} - 6 x 5 y^{2} - 3 x + 19 + 27 x + 5 y^{2} - 10 5 y^{2} - 3 x + 19 + 44

求解步骤

(3 x - 5 y^{2} - 3 x + 19 + 5)^{2}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(3 x - 5 y^{2} - 3 x + 19 + 5)^{2} = (3 x - 5 y^{2} - 3 x + 19 + 5) (3 x - 5 y^{2} - 3 x + 19 + 5)

= (3 x - 5 y^{2} - 3 x + 19 + 5) (3 x - 5 y^{2} - 3 x + 19 + 5)

打开括号

= 3 x \cdot 3 x + 3 x (- 5 y^{2} - 3 x + 19) + 3 x \cdot 5 - 5 y^{2} - 3 x + 19 \cdot 3 x - 5 y^{2} - 3 x + 19 (- 5 y^{2} - 3 x + 19) - 5 y^{2} - 3 x + 19 \cdot 5 + 5 \cdot 3 x + 5 (- 5 y^{2} - 3 x + 19) + 5 \cdot 5

化简

3 x \cdot 3 x + 3 x (- 5 y^{2} - 3 x + 19) + 3 x \cdot 5 - 5 y^{2} - 3 x + 19 \cdot 3 x - 5 y^{2} - 3 x + 19 (- 5 y^{2} - 3 x + 19) - 5 y^{2} - 3 x + 19 \cdot 5 + 5 \cdot 3 x + 5 (- 5 y^{2} - 3 x + 19) + 5 \cdot 5 : 9 x^{2} - 6 x 5 y^{2} - 3 x + 19 + 27 x + 5 y^{2} - 10 5 y^{2} - 3 x + 19 + 44

= 9 x^{2} - 6 x 5 y^{2} - 3 x + 19 + 27 x + 5 y^{2} - 10 5 y^{2} - 3 x + 19 + 44

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