Solve 1/16-4x^2/49=

$$\frac { 1 } { 16 } - \frac { 4 x ^ { 2 } } { 49 } =$$

Evaluate

$$-\frac{4x^{2}}{49}+\frac{1}{16}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 49 is 784. Multiply \frac{1}{16} times \frac{49}{49}. Multiply \frac{4x^{2}}{49} times \frac{16}{16}.

$$\frac{49}{784}-\frac{16\times 4x^{2}}{784}$$

Since \frac{49}{784} and \frac{16\times 4x^{2}}{784} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49-16\times 4x^{2}}{784}$$

Do the multiplications in 49-16\times 4x^{2}.

$$\frac{49-64x^{2}}{784}$$

Factor

$$\frac{\left(-8x-7\right)\left(8x-7\right)}{784}$$

Solution Steps

Factor out \frac{1}{784}.

$$\frac{49-64x^{2}}{784}$$

Consider 49-64x^{2}. Rewrite 49-64x^{2} as 7^{2}-\left(8x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7-8x\right)\left(7+8x\right)$$

Reorder the terms.

$$\left(-8x+7\right)\left(8x+7\right)$$

Rewrite the complete factored expression.

$$\frac{\left(-8x+7\right)\left(8x+7\right)}{784}$$