Solve 1/3-3x^2/4

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{1}{3} times \frac{4}{4}. Multiply \frac{3x^{2}}{4} times \frac{3}{3}.

$$\frac{4}{12}-\frac{3\times 3x^{2}}{12}$$

Since \frac{4}{12} and \frac{3\times 3x^{2}}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3\times 3x^{2}}{12}$$

Do the multiplications in 4-3\times 3x^{2}.

$$\frac{4-9x^{2}}{12}$$

Factor

$$\frac{\left(-3x-2\right)\left(3x-2\right)}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{4-9x^{2}}{12}$$

Consider 4-9x^{2}. Rewrite 4-9x^{2} as 2^{2}-\left(3x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2-3x\right)\left(2+3x\right)$$

Reorder the terms.

$$\left(-3x+2\right)\left(3x+2\right)$$

Rewrite the complete factored expression.

$$\frac{\left(-3x+2\right)\left(3x+2\right)}{12}$$