Solve 16/25-(2x+1)(2x-1)=

$$\frac{ 16 }{ 25 } -(2x+1)(2x-1)=$$

Evaluate

$$\frac{41}{25}-4x^{2}$$

Solution Steps

Consider \left(2x+1\right)\left(2x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{16}{25}-\left(\left(2x\right)^{2}-1^{2}\right)$$

Expand \left(2x\right)^{2}.

$$\frac{16}{25}-\left(2^{2}x^{2}-1^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16}{25}-\left(4x^{2}-1^{2}\right)$$

Calculate 1 to the power of 2 and get 1.

$$\frac{16}{25}-\left(4x^{2}-1\right)$$

To find the opposite of 4x^{2}-1, find the opposite of each term.

$$\frac{16}{25}-4x^{2}-\left(-1\right)$$

The opposite of -1 is 1.

$$\frac{16}{25}-4x^{2}+1$$

Convert 1 to fraction \frac{25}{25}.

$$\frac{16}{25}-4x^{2}+\frac{25}{25}$$

Since \frac{16}{25} and \frac{25}{25} have the same denominator, add them by adding their numerators.

$$\frac{16+25}{25}-4x^{2}$$

Add 16 and 25 to get 41.

$$\frac{41}{25}-4x^{2}$$

Expand

$$\frac{41}{25}-4x^{2}$$

Solution Steps

Consider \left(2x+1\right)\left(2x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{16}{25}-\left(\left(2x\right)^{2}-1^{2}\right)$$

Expand \left(2x\right)^{2}.

$$\frac{16}{25}-\left(2^{2}x^{2}-1^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16}{25}-\left(4x^{2}-1^{2}\right)$$

Calculate 1 to the power of 2 and get 1.

$$\frac{16}{25}-\left(4x^{2}-1\right)$$

To find the opposite of 4x^{2}-1, find the opposite of each term.

$$\frac{16}{25}-4x^{2}-\left(-1\right)$$

The opposite of -1 is 1.

$$\frac{16}{25}-4x^{2}+1$$

Convert 1 to fraction \frac{25}{25}.

$$\frac{16}{25}-4x^{2}+\frac{25}{25}$$

Since \frac{16}{25} and \frac{25}{25} have the same denominator, add them by adding their numerators.

$$\frac{16+25}{25}-4x^{2}$$

Add 16 and 25 to get 41.

$$\frac{41}{25}-4x^{2}$$