Solve 8100*(300*x)+(300xx(x+1)/2*12*12/100)

$$8100 \cdot ( 300 \times x ) + ( 300 x \frac { x ( x + 1 ) } { 2 \times 12 } \times \frac { 12 } { 100 } )$$

Evaluate

$$\frac{3x\left(x^{2}+x+1620000\right)}{2}$$

Short Solution Steps

Multiply 8100 and 300 to get 2430000.

$$2430000x+300x\times \frac{x\left(x+1\right)}{2\times 12}\times \frac{12}{100}$$

Multiply 2 and 12 to get 24.

$$2430000x+300x\times \frac{x\left(x+1\right)}{24}\times \frac{12}{100}$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$2430000x+300x\times \frac{x\left(x+1\right)}{24}\times \frac{3}{25}$$

Express 300\times \frac{3}{25} as a single fraction.

$$2430000x+\frac{300\times 3}{25}x\times \frac{x\left(x+1\right)}{24}$$

Multiply 300 and 3 to get 900.

$$2430000x+\frac{900}{25}x\times \frac{x\left(x+1\right)}{24}$$

Divide 900 by 25 to get 36.

$$2430000x+36x\times \frac{x\left(x+1\right)}{24}$$

Use the distributive property to multiply x by x+1.

$$2430000x+36x\times \frac{x^{2}+x}{24}$$

Express 36\times \frac{x^{2}+x}{24} as a single fraction.

$$2430000x+\frac{36\left(x^{2}+x\right)}{24}x$$

Use the distributive property to multiply 36 by x^{2}+x.

$$2430000x+\frac{36x^{2}+36x}{24}x$$

Express \frac{36x^{2}+36x}{24}x as a single fraction.

$$2430000x+\frac{\left(36x^{2}+36x\right)x}{24}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2430000x times \frac{24}{24}.

$$\frac{24\times 2430000x}{24}+\frac{\left(36x^{2}+36x\right)x}{24}$$

Since \frac{24\times 2430000x}{24} and \frac{\left(36x^{2}+36x\right)x}{24} have the same denominator, add them by adding their numerators.

$$\frac{24\times 2430000x+\left(36x^{2}+36x\right)x}{24}$$

Do the multiplications in 24\times 2430000x+\left(36x^{2}+36x\right)x.

$$\frac{58320000x+36x^{3}+36x^{2}}{24}$$

Expand

$$\frac{3x^{3}}{2}+\frac{3x^{2}}{2}+2430000x$$

Short Solution Steps

Multiply 8100 and 300 to get 2430000.

$$2430000x+300x\times \frac{x\left(x+1\right)}{2\times 12}\times \frac{12}{100}$$

Multiply 2 and 12 to get 24.

$$2430000x+300x\times \frac{x\left(x+1\right)}{24}\times \frac{12}{100}$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$2430000x+300x\times \frac{x\left(x+1\right)}{24}\times \frac{3}{25}$$

Express 300\times \frac{3}{25} as a single fraction.

$$2430000x+\frac{300\times 3}{25}x\times \frac{x\left(x+1\right)}{24}$$

Multiply 300 and 3 to get 900.

$$2430000x+\frac{900}{25}x\times \frac{x\left(x+1\right)}{24}$$

Divide 900 by 25 to get 36.

$$2430000x+36x\times \frac{x\left(x+1\right)}{24}$$

Use the distributive property to multiply x by x+1.

$$2430000x+36x\times \frac{x^{2}+x}{24}$$

Express 36\times \frac{x^{2}+x}{24} as a single fraction.

$$2430000x+\frac{36\left(x^{2}+x\right)}{24}x$$

Use the distributive property to multiply 36 by x^{2}+x.

$$2430000x+\frac{36x^{2}+36x}{24}x$$

Express \frac{36x^{2}+36x}{24}x as a single fraction.

$$2430000x+\frac{\left(36x^{2}+36x\right)x}{24}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2430000x times \frac{24}{24}.

$$\frac{24\times 2430000x}{24}+\frac{\left(36x^{2}+36x\right)x}{24}$$

Since \frac{24\times 2430000x}{24} and \frac{\left(36x^{2}+36x\right)x}{24} have the same denominator, add them by adding their numerators.

$$\frac{24\times 2430000x+\left(36x^{2}+36x\right)x}{24}$$

Do the multiplications in 24\times 2430000x+\left(36x^{2}+36x\right)x.

$$\frac{58320000x+36x^{3}+36x^{2}}{24}$$