Solve {left(0.000003x^6-0.0002x^5+0.002x^4+0.0033x^3-0.2289{x}^2+1.2422x+0.9852right)}^2

$${ \left(0.000003 { x }^{ 6 } -0.0002 { x }^{ 5 } +0.002 { x }^{ 4 } +0.0033 { x }^{ 3 } -0.2289 { x }^{ 2 } +1.2422x+0.9852 \right) }^{ 2 }$$

Evaluate

$$\left(\frac{3x^{6}}{1000000}-\frac{x^{5}}{5000}+\frac{x^{4}}{500}+\frac{33x^{3}}{10000}-\frac{2289x^{2}}{10000}+\frac{6211x}{5000}+0.9852\right)^{2}$$

Solution Steps

Square 0.000003x^{6}-0.0002x^{5}+0.002x^{4}+0.0033x^{3}-0.2289x^{2}+1.2422x+0.9852.

$$0.000000000009x^{12}-0.0000000012x^{11}+0.000000052x^{10}-0.0000007802x^{9}+0.0000013066x^{8}+0.0001122132x^{7}-0.0013956788x^{6}+0.00306398x^{5}+0.06453453x^{4}-0.56217684x^{3}+1.09203628x^{2}+2.44763088x+0.97061904$$

Expand

$$\frac{9x^{12}}{1000000000000}-\frac{3x^{11}}{2500000000}+\frac{13x^{10}}{250000000}-\frac{3901x^{9}}{5000000000}+\frac{6533x^{8}}{5000000000}+\frac{280533x^{7}}{2500000000}-\frac{3489197x^{6}}{2500000000}+\frac{153199x^{5}}{50000000}+\frac{6453453x^{4}}{100000000}-\frac{14054421x^{3}}{25000000}+\frac{27300907x^{2}}{25000000}+\frac{15297693x}{6250000}+0.97061904$$

Solution Steps

Square 0.000003x^{6}-0.0002x^{5}+0.002x^{4}+0.0033x^{3}-0.2289x^{2}+1.2422x+0.9852.

$$0.000000000009x^{12}-0.0000000012x^{11}+0.000000052x^{10}-0.0000007802x^{9}+0.0000013066x^{8}+0.0001122132x^{7}-0.0013956788x^{6}+0.00306398x^{5}+0.06453453x^{4}-0.56217684x^{3}+1.09203628x^{2}+2.44763088x+0.97061904$$