Solve 6left(1-x^9right)^2-12left(1-x^9right)+6

$$6 { \left(1- { x }^{ 9 } \right) }^{ 2 } -12 \left( 1- { x }^{ 9 } \right) +6$$

Evaluate

$$6x^{18}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x^{9}\right)^{2}.

$$6\left(1-2x^{9}+\left(x^{9}\right)^{2}\right)-12\left(1-x^{9}\right)+6$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$6\left(1-2x^{9}+x^{18}\right)-12\left(1-x^{9}\right)+6$$

Use the distributive property to multiply 6 by 1-2x^{9}+x^{18}.

$$6-12x^{9}+6x^{18}-12\left(1-x^{9}\right)+6$$

Use the distributive property to multiply -12 by 1-x^{9}.

$$6-12x^{9}+6x^{18}-12+12x^{9}+6$$

Subtract 12 from 6 to get -6.

$$-6-12x^{9}+6x^{18}+12x^{9}+6$$

Combine -12x^{9} and 12x^{9} to get 0.

$$-6+6x^{18}+6$$

Add -6 and 6 to get 0.

$$6x^{18}$$

Expand

$$6x^{18}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x^{9}\right)^{2}.

$$6\left(1-2x^{9}+\left(x^{9}\right)^{2}\right)-12\left(1-x^{9}\right)+6$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$6\left(1-2x^{9}+x^{18}\right)-12\left(1-x^{9}\right)+6$$

Use the distributive property to multiply 6 by 1-2x^{9}+x^{18}.

$$6-12x^{9}+6x^{18}-12\left(1-x^{9}\right)+6$$

Use the distributive property to multiply -12 by 1-x^{9}.

$$6-12x^{9}+6x^{18}-12+12x^{9}+6$$

Subtract 12 from 6 to get -6.

$$-6-12x^{9}+6x^{18}+12x^{9}+6$$

Combine -12x^{9} and 12x^{9} to get 0.

$$-6+6x^{18}+6$$

Add -6 and 6 to get 0.

$$6x^{18}$$