Solve 81x^2/4-1/49

$$\frac{ 81 { x }^{ 2 } }{ 4 } - \frac{ 1 }{ 49 }$$

Factor

$$\frac{\left(63x-2\right)\left(63x+2\right)}{196}$$

Solution Steps

Factor out \frac{1}{196}.

$$\frac{3969x^{2}-4}{196}$$

Consider 3969x^{2}-4. Rewrite 3969x^{2}-4 as \left(63x\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(63x-2\right)\left(63x+2\right)$$

Rewrite the complete factored expression.

$$\frac{\left(63x-2\right)\left(63x+2\right)}{196}$$

Evaluate

$$\frac{81x^{2}}{4}-\frac{1}{49}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 49 is 196. Multiply \frac{81x^{2}}{4} times \frac{49}{49}. Multiply \frac{1}{49} times \frac{4}{4}.

$$\frac{49\times 81x^{2}}{196}-\frac{4}{196}$$

Since \frac{49\times 81x^{2}}{196} and \frac{4}{196} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49\times 81x^{2}-4}{196}$$

Do the multiplications in 49\times 81x^{2}-4.

$$\frac{3969x^{2}-4}{196}$$