Solve 30*9^2+20x^3y^primediv101^2y=

$$30 \times 9 ^ { 2 } + 20 x ^ { 3 } y ^ { \prime } \div 101 ^ { 2 } y =$$

Factor

$$2\times 3^{5}\times 5$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$factor(30\times 81+\frac{20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)}{101^{2}}y)$$

Multiply 30 and 81 to get 2430.

$$factor(2430+\frac{20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)}{101^{2}}y)$$

Calculate 101 to the power of 2 and get 10201.

$$factor(2430+\frac{20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)}{10201}y)$$

Express \frac{20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)}{10201}y as a single fraction.

$$factor(2430+\frac{20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y}{10201})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2430 times \frac{10201}{10201}.

$$factor(\frac{2430\times 10201}{10201}+\frac{20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y}{10201})$$

Since \frac{2430\times 10201}{10201} and \frac{20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y}{10201} have the same denominator, add them by adding their numerators.

$$factor(\frac{2430\times 10201+20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y}{10201})$$

Multiply 2430 and 10201 to get 24788430.

$$factor(\frac{24788430+20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y}{10201})$$

Consider 24788430+20x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y. Factor out 10.

$$10\left(2478843+2x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{10\left(2478843+2x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(y)y\right)}{10201}$$

Evaluate

$$2430$$