Solve f(x)=3(x+6)^2-75

$$f ( x ) = 3 ( x + 6 ) ^ { 2 } - 75$$

Evaluate

$$3\left(x+1\right)\left(x+11\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$3\left(x^{2}+12x+36\right)-75$$

Use the distributive property to multiply 3 by x^{2}+12x+36.

$$3x^{2}+36x+108-75$$

Subtract 75 from 108 to get 33.

$$3x^{2}+36x+33$$

Expand

$$3x^{2}+36x+33$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$3\left(x^{2}+12x+36\right)-75$$

Use the distributive property to multiply 3 by x^{2}+12x+36.

$$3x^{2}+36x+108-75$$

Subtract 75 from 108 to get 33.

$$3x^{2}+36x+33$$