Solve (2a-3a)^2-[(1/2x+1/2x)^2]^3-4

$$( 2 a - 3 a ) ^ { 2 } - [ ( \frac { 1 } { 2 } x + \frac { 1 } { 2 } x ) ^ { 2 } ] ^ { 3 } - 4$$

Evaluate

$$-x^{6}+a^{2}-4$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(2a-3a\right)^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Combine 2a and -3a to get -a.

$$\left(-a\right)^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Expand \left(-a\right)^{2}.

$$\left(-1\right)^{2}a^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Calculate -1 to the power of 2 and get 1.

$$1a^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$1a^{2}-x^{6}-4$$

For any term t, t\times 1=t and 1t=t.

$$a^{2}-x^{6}-4$$

Expand

$$-x^{6}+a^{2}-4$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(2a-3a\right)^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Combine 2a and -3a to get -a.

$$\left(-a\right)^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Expand \left(-a\right)^{2}.

$$\left(-1\right)^{2}a^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Calculate -1 to the power of 2 and get 1.

$$1a^{2}-\left(\frac{1}{2}x+\frac{1}{2}x\right)^{6}-4$$

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$1a^{2}-x^{6}-4$$

For any term t, t\times 1=t and 1t=t.

$$a^{2}-x^{6}-4$$