Solve left(x+0.1right)left(x-0.5right)left(x-0.9right)left(x-1.2right)

$$\left( x+0.1 \right) \left( x-0.5 \right) \left( x-0.9 \right) \left( x-1.2 \right)$$

Evaluate

$$\left(x-1.2\right)\left(x-0.9\right)\left(x-0.5\right)\left(x+0.1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+0.1 by each term of x-0.5.

$$\left(x^{2}-0.5x+0.1x-0.05\right)\left(x-0.9\right)\left(x-1.2\right)$$

Combine -0.5x and 0.1x to get -0.4x.

$$\left(x^{2}-0.4x-0.05\right)\left(x-0.9\right)\left(x-1.2\right)$$

Apply the distributive property by multiplying each term of x^{2}-0.4x-0.05 by each term of x-0.9.

$$\left(x^{3}-0.9x^{2}-0.4x^{2}+0.36x-0.05x+0.045\right)\left(x-1.2\right)$$

Combine -0.9x^{2} and -0.4x^{2} to get -1.3x^{2}.

$$\left(x^{3}-1.3x^{2}+0.36x-0.05x+0.045\right)\left(x-1.2\right)$$

Combine 0.36x and -0.05x to get 0.31x.

$$\left(x^{3}-1.3x^{2}+0.31x+0.045\right)\left(x-1.2\right)$$

Apply the distributive property by multiplying each term of x^{3}-1.3x^{2}+0.31x+0.045 by each term of x-1.2.

$$x^{4}-1.2x^{3}-1.3x^{3}+1.56x^{2}+0.31x^{2}-0.372x+0.045x-0.054$$

Combine -1.2x^{3} and -1.3x^{3} to get -2.5x^{3}.

$$x^{4}-2.5x^{3}+1.56x^{2}+0.31x^{2}-0.372x+0.045x-0.054$$

Combine 1.56x^{2} and 0.31x^{2} to get 1.87x^{2}.

$$x^{4}-2.5x^{3}+1.87x^{2}-0.372x+0.045x-0.054$$

Combine -0.372x and 0.045x to get -0.327x.

$$x^{4}-2.5x^{3}+1.87x^{2}-0.327x-0.054$$

Expand

$$x^{4}-\frac{5x^{3}}{2}+\frac{187x^{2}}{100}-\frac{327x}{1000}-0.054$$

Solution Steps

Apply the distributive property by multiplying each term of x+0.1 by each term of x-0.5.

$$\left(x^{2}-0.5x+0.1x-0.05\right)\left(x-0.9\right)\left(x-1.2\right)$$

Combine -0.5x and 0.1x to get -0.4x.

$$\left(x^{2}-0.4x-0.05\right)\left(x-0.9\right)\left(x-1.2\right)$$

Apply the distributive property by multiplying each term of x^{2}-0.4x-0.05 by each term of x-0.9.

$$\left(x^{3}-0.9x^{2}-0.4x^{2}+0.36x-0.05x+0.045\right)\left(x-1.2\right)$$

Combine -0.9x^{2} and -0.4x^{2} to get -1.3x^{2}.

$$\left(x^{3}-1.3x^{2}+0.36x-0.05x+0.045\right)\left(x-1.2\right)$$

Combine 0.36x and -0.05x to get 0.31x.

$$\left(x^{3}-1.3x^{2}+0.31x+0.045\right)\left(x-1.2\right)$$

Apply the distributive property by multiplying each term of x^{3}-1.3x^{2}+0.31x+0.045 by each term of x-1.2.

$$x^{4}-1.2x^{3}-1.3x^{3}+1.56x^{2}+0.31x^{2}-0.372x+0.045x-0.054$$

Combine -1.2x^{3} and -1.3x^{3} to get -2.5x^{3}.

$$x^{4}-2.5x^{3}+1.56x^{2}+0.31x^{2}-0.372x+0.045x-0.054$$

Combine 1.56x^{2} and 0.31x^{2} to get 1.87x^{2}.

$$x^{4}-2.5x^{3}+1.87x^{2}-0.372x+0.045x-0.054$$

Combine -0.372x and 0.045x to get -0.327x.

$$x^{4}-2.5x^{3}+1.87x^{2}-0.327x-0.054$$