Solve 25x^4/36-x^2/3+1/25

$$\frac { 25 x ^ { 4 } } { 36 } - \frac { x ^ { 2 } } { 3 } + \frac { 1 } { 25 }$$

Evaluate

$$\frac{\left(25x^{2}-6\right)^{2}}{900}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 3 is 36. Multiply \frac{x^{2}}{3} times \frac{12}{12}.

$$\frac{25x^{4}}{36}-\frac{12x^{2}}{36}+\frac{1}{25}$$

Since \frac{25x^{4}}{36} and \frac{12x^{2}}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25x^{4}-12x^{2}}{36}+\frac{1}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 25 is 900. Multiply \frac{25x^{4}-12x^{2}}{36} times \frac{25}{25}. Multiply \frac{1}{25} times \frac{36}{36}.

$$\frac{25\left(25x^{4}-12x^{2}\right)}{900}+\frac{36}{900}$$

Since \frac{25\left(25x^{4}-12x^{2}\right)}{900} and \frac{36}{900} have the same denominator, add them by adding their numerators.

$$\frac{25\left(25x^{4}-12x^{2}\right)+36}{900}$$

Do the multiplications in 25\left(25x^{4}-12x^{2}\right)+36.

$$\frac{625x^{4}-300x^{2}+36}{900}$$

Factor

$$\frac{\left(25x^{2}-6\right)^{2}}{900}$$

Solution Steps

Factor out \frac{1}{900}.

$$\frac{625x^{4}-300x^{2}+36}{900}$$

Consider 625x^{4}-300x^{2}+36. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=25x^{2} and b=6.

$$\left(25x^{2}-6\right)^{2}$$

Rewrite the complete factored expression. Polynomial 25x^{2}-6 is not factored since it does not have any rational roots.

$$\frac{\left(25x^{2}-6\right)^{2}}{900}$$