Solve 1+1.107x+0.61275xleft(x-0.2right)+0.22625xleft(x-0.2right)left(x-0.4right)+0.061975xleft(x-0.2right)left(x-0.4right)left(x-0.6right)

$$1+1.107x+0.61275x \left( x-0.2 \right) +0.22625x \left( x-0.2 \right) \left( x-0.4 \right) +0.061975x \left( x-0.2 \right) \left( x-0.4 \right) \left( x-0.6 \right)$$

Evaluate

$$\frac{2479x^{4}}{40000}+\frac{3797x^{3}}{25000}+\frac{504269x^{2}}{1000000}+\frac{1249469x}{1250000}+1$$

Solution Steps

Use the distributive property to multiply 0.61275x by x-0.2.

$$1+1.107x+0.61275x^{2}-0.12255x+0.22625x\left(x-0.2\right)\left(x-0.4\right)+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine 1.107x and -0.12255x to get 0.98445x.

$$1+0.98445x+0.61275x^{2}+0.22625x\left(x-0.2\right)\left(x-0.4\right)+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Use the distributive property to multiply 0.22625x by x-0.2.

$$1+0.98445x+0.61275x^{2}+\left(0.22625x^{2}-0.04525x\right)\left(x-0.4\right)+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Apply the distributive property by multiplying each term of 0.22625x^{2}-0.04525x by each term of x-0.4.

$$1+0.98445x+0.61275x^{2}+0.22625x^{3}-0.0905x^{2}-0.04525x^{2}+0.0181x+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine -0.0905x^{2} and -0.04525x^{2} to get -0.13575x^{2}.

$$1+0.98445x+0.61275x^{2}+0.22625x^{3}-0.13575x^{2}+0.0181x+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine 0.61275x^{2} and -0.13575x^{2} to get 0.477x^{2}.

$$1+0.98445x+0.477x^{2}+0.22625x^{3}+0.0181x+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine 0.98445x and 0.0181x to get 1.00255x.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Use the distributive property to multiply 0.061975x by x-0.2.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+\left(0.061975x^{2}-0.012395x\right)\left(x-0.4\right)\left(x-0.6\right)$$

Apply the distributive property by multiplying each term of 0.061975x^{2}-0.012395x by each term of x-0.4.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+\left(0.061975x^{3}-0.02479x^{2}-0.012395x^{2}+0.004958x\right)\left(x-0.6\right)$$

Combine -0.02479x^{2} and -0.012395x^{2} to get -0.037185x^{2}.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+\left(0.061975x^{3}-0.037185x^{2}+0.004958x\right)\left(x-0.6\right)$$

Apply the distributive property by multiplying each term of 0.061975x^{3}-0.037185x^{2}+0.004958x by each term of x-0.6.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x^{4}-0.037185x^{3}-0.037185x^{3}+0.022311x^{2}+0.004958x^{2}-0.0029748x$$

Combine -0.037185x^{3} and -0.037185x^{3} to get -0.07437x^{3}.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x^{4}-0.07437x^{3}+0.022311x^{2}+0.004958x^{2}-0.0029748x$$

Combine 0.022311x^{2} and 0.004958x^{2} to get 0.027269x^{2}.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x^{4}-0.07437x^{3}+0.027269x^{2}-0.0029748x$$

Combine 0.22625x^{3} and -0.07437x^{3} to get 0.15188x^{3}.

$$1+1.00255x+0.477x^{2}+0.15188x^{3}+0.061975x^{4}+0.027269x^{2}-0.0029748x$$

Combine 0.477x^{2} and 0.027269x^{2} to get 0.504269x^{2}.

$$1+1.00255x+0.504269x^{2}+0.15188x^{3}+0.061975x^{4}-0.0029748x$$

Combine 1.00255x and -0.0029748x to get 0.9995752x.

$$1+0.9995752x+0.504269x^{2}+0.15188x^{3}+0.061975x^{4}$$

Expand

$$\frac{2479x^{4}}{40000}+\frac{3797x^{3}}{25000}+\frac{504269x^{2}}{1000000}+\frac{1249469x}{1250000}+1$$

Solution Steps

Use the distributive property to multiply 0.61275x by x-0.2.

$$1+1.107x+0.61275x^{2}-0.12255x+0.22625x\left(x-0.2\right)\left(x-0.4\right)+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine 1.107x and -0.12255x to get 0.98445x.

$$1+0.98445x+0.61275x^{2}+0.22625x\left(x-0.2\right)\left(x-0.4\right)+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Use the distributive property to multiply 0.22625x by x-0.2.

$$1+0.98445x+0.61275x^{2}+\left(0.22625x^{2}-0.04525x\right)\left(x-0.4\right)+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Apply the distributive property by multiplying each term of 0.22625x^{2}-0.04525x by each term of x-0.4.

$$1+0.98445x+0.61275x^{2}+0.22625x^{3}-0.0905x^{2}-0.04525x^{2}+0.0181x+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine -0.0905x^{2} and -0.04525x^{2} to get -0.13575x^{2}.

$$1+0.98445x+0.61275x^{2}+0.22625x^{3}-0.13575x^{2}+0.0181x+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine 0.61275x^{2} and -0.13575x^{2} to get 0.477x^{2}.

$$1+0.98445x+0.477x^{2}+0.22625x^{3}+0.0181x+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Combine 0.98445x and 0.0181x to get 1.00255x.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x\left(x-0.2\right)\left(x-0.4\right)\left(x-0.6\right)$$

Use the distributive property to multiply 0.061975x by x-0.2.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+\left(0.061975x^{2}-0.012395x\right)\left(x-0.4\right)\left(x-0.6\right)$$

Apply the distributive property by multiplying each term of 0.061975x^{2}-0.012395x by each term of x-0.4.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+\left(0.061975x^{3}-0.02479x^{2}-0.012395x^{2}+0.004958x\right)\left(x-0.6\right)$$

Combine -0.02479x^{2} and -0.012395x^{2} to get -0.037185x^{2}.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+\left(0.061975x^{3}-0.037185x^{2}+0.004958x\right)\left(x-0.6\right)$$

Apply the distributive property by multiplying each term of 0.061975x^{3}-0.037185x^{2}+0.004958x by each term of x-0.6.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x^{4}-0.037185x^{3}-0.037185x^{3}+0.022311x^{2}+0.004958x^{2}-0.0029748x$$

Combine -0.037185x^{3} and -0.037185x^{3} to get -0.07437x^{3}.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x^{4}-0.07437x^{3}+0.022311x^{2}+0.004958x^{2}-0.0029748x$$

Combine 0.022311x^{2} and 0.004958x^{2} to get 0.027269x^{2}.

$$1+1.00255x+0.477x^{2}+0.22625x^{3}+0.061975x^{4}-0.07437x^{3}+0.027269x^{2}-0.0029748x$$

Combine 0.22625x^{3} and -0.07437x^{3} to get 0.15188x^{3}.

$$1+1.00255x+0.477x^{2}+0.15188x^{3}+0.061975x^{4}+0.027269x^{2}-0.0029748x$$

Combine 0.477x^{2} and 0.027269x^{2} to get 0.504269x^{2}.

$$1+1.00255x+0.504269x^{2}+0.15188x^{3}+0.061975x^{4}-0.0029748x$$

Combine 1.00255x and -0.0029748x to get 0.9995752x.

$$1+0.9995752x+0.504269x^{2}+0.15188x^{3}+0.061975x^{4}$$