Solve f(x)=x^2-(3x+1)^2

$$f ( x ) = x ^ { 2 } - ( 3 x + 1 ) ^ { 2 }$$

Evaluate

$$-8x^{2}-6x-1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+1\right)^{2}.

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

To find the opposite of 9x^{2}+6x+1, find the opposite of each term.

$$x^{2}-9x^{2}-6x-1$$

Combine x^{2} and -9x^{2} to get -8x^{2}.

$$-8x^{2}-6x-1$$

Expand

$$-8x^{2}-6x-1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+1\right)^{2}.

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

To find the opposite of 9x^{2}+6x+1, find the opposite of each term.

$$x^{2}-9x^{2}-6x-1$$

Combine x^{2} and -9x^{2} to get -8x^{2}.

$$-8x^{2}-6x-1$$