Solve f(x)=2(x+9)^2-6

$$f ( x ) = 2 ( x + 9 ) ^ { 2 } - 6$$

Evaluate

$$2\left(\left(x+9\right)^{2}-3\right)$$

Solution Steps

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

$$2\left(x^{2}+18x+81\right)-6$$

Use the distributive property to multiply 2 by x^{2}+18x+81.

$$2x^{2}+36x+162-6$$

Subtract 6 from 162 to get 156.

$$2x^{2}+36x+156$$

Expand

$$2x^{2}+36x+156$$

Solution Steps

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

$$2\left(x^{2}+18x+81\right)-6$$

Use the distributive property to multiply 2 by x^{2}+18x+81.

$$2x^{2}+36x+162-6$$

Subtract 6 from 162 to get 156.

$$2x^{2}+36x+156$$