求解 (x+5)^2+2(x+5)(y-1)+(y-1)^2 | Microsoft Math Solver

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x^{2}+10x+25+2\left(x+5\right)\left(y-1\right)+\left(y-1\right)^{2}

使用二项式定理 \left(a+b\right)^{2}=a^{2}+2ab+b^{2} 展开 \left(x+5\right)^{2}。

x^{2}+10x+25+\left(2x+10\right)\left(y-1\right)+\left(y-1\right)^{2}

使用分配律将 2 乘以 x+5。

x^{2}+10x+25+2xy-2x+10y-10+\left(y-1\right)^{2}

使用分配律将 2x+10 乘以 y-1。

x^{2}+8x+25+2xy+10y-10+\left(y-1\right)^{2}

合并 10x 和 -2x，得到 8x。

x^{2}+8x+15+2xy+10y+\left(y-1\right)^{2}

将 25 减去 10，得到 15。

x^{2}+8x+15+2xy+10y+y^{2}-2y+1

使用二项式定理 \left(a-b\right)^{2}=a^{2}-2ab+b^{2} 展开 \left(y-1\right)^{2}。

x^{2}+8x+15+2xy+8y+y^{2}+1

合并 10y 和 -2y，得到 8y。

x^{2}+8x+16+2xy+8y+y^{2}

15 与 1 相加，得到 16。