Solve f(x)=4(x+6)^2-3

$$f ( x ) = 4 ( x + 6 ) ^ { 2 } - 3$$

Evaluate

$$4\left(x+6\right)^{2}-3$$

Solution Steps

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

$$4\left(x^{2}+12x+36\right)-3$$

Use the distributive property to multiply 4 by x^{2}+12x+36.

$$4x^{2}+48x+144-3$$

Subtract 3 from 144 to get 141.

$$4x^{2}+48x+141$$

Expand

$$4x^{2}+48x+141$$

Solution Steps

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

$$4\left(x^{2}+12x+36\right)-3$$

Use the distributive property to multiply 4 by x^{2}+12x+36.

$$4x^{2}+48x+144-3$$

Subtract 3 from 144 to get 141.

$$4x^{2}+48x+141$$