Solve 5x^2-25/85-5

$$5 { x }^{ 2 } - \frac{ 25 }{ 85-5 }$$

Evaluate

$$5x^{2}-\frac{5}{16}$$

Solution Steps

Subtract 5 from 85 to get 80.

$$5x^{2}-\frac{25}{80}$$

Reduce the fraction \frac{25}{80} to lowest terms by extracting and canceling out 5.

$$5x^{2}-\frac{5}{16}$$

Factor

$$\frac{5\left(4x-1\right)\left(4x+1\right)}{16}$$

Solution Steps

Subtract 5 from 85 to get 80.

$$factor(5x^{2}-\frac{25}{80})$$

Reduce the fraction \frac{25}{80} to lowest terms by extracting and canceling out 5.

$$factor(5x^{2}-\frac{5}{16})$$

Factor out \frac{5}{16}.

$$\frac{5\left(16x^{2}-1\right)}{16}$$

Consider 16x^{2}-1. Rewrite 16x^{2}-1 as \left(4x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x-1\right)\left(4x+1\right)$$

Rewrite the complete factored expression.

$$\frac{5\left(4x-1\right)\left(4x+1\right)}{16}$$