Solve ((n+3)^2-27(n+3)^2)

$$( ( n + 3 ) ^ { 2 } - 27 ( n + 3 ) ^ { 2 } )$$

Evaluate

$$-26\left(n+3\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+3\right)^{2}.

$$n^{2}+6n+9-27\left(n+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+3\right)^{2}.

$$n^{2}+6n+9-27\left(n^{2}+6n+9\right)$$

Use the distributive property to multiply -27 by n^{2}+6n+9.

$$n^{2}+6n+9-27n^{2}-162n-243$$

Combine n^{2} and -27n^{2} to get -26n^{2}.

$$-26n^{2}+6n+9-162n-243$$

Combine 6n and -162n to get -156n.

$$-26n^{2}-156n+9-243$$

Subtract 243 from 9 to get -234.

$$-26n^{2}-156n-234$$

Expand

$$-26n^{2}-156n-234$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+3\right)^{2}.

$$n^{2}+6n+9-27\left(n+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+3\right)^{2}.

$$n^{2}+6n+9-27\left(n^{2}+6n+9\right)$$

Use the distributive property to multiply -27 by n^{2}+6n+9.

$$n^{2}+6n+9-27n^{2}-162n-243$$

Combine n^{2} and -27n^{2} to get -26n^{2}.

$$-26n^{2}+6n+9-162n-243$$

Combine 6n and -162n to get -156n.

$$-26n^{2}-156n+9-243$$

Subtract 243 from 9 to get -234.

$$-26n^{2}-156n-234$$