Solve ((2-a)*(2+a)-2)^3

$$( ( 2 - a ) \times ( 2 + a ) - 2 ) ^ { 3 }$$

Evaluate

$$\left(2-a^{2}\right)^{3}$$

Solution Steps

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

$$\left(4-a^{2}-2\right)^{3}$$

Subtract 2 from 4 to get 2.

$$\left(2-a^{2}\right)^{3}$$

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(2-a^{2}\right)^{3}.

$$8-12a^{2}+6\left(a^{2}\right)^{2}-\left(a^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$8-12a^{2}+6a^{4}-\left(a^{2}\right)^{3}$$

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

$$8-12a^{2}+6a^{4}-a^{6}$$

Expand

$$8-12a^{2}+6a^{4}-a^{6}$$

Solution Steps

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

$$\left(4-a^{2}-2\right)^{3}$$

Subtract 2 from 4 to get 2.

$$\left(2-a^{2}\right)^{3}$$

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(2-a^{2}\right)^{3}.

$$8-12a^{2}+6\left(a^{2}\right)^{2}-\left(a^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$8-12a^{2}+6a^{4}-\left(a^{2}\right)^{3}$$

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

$$8-12a^{2}+6a^{4}-a^{6}$$