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Question

# Let f(x) = (2x - 3)(2x + 3). What are the constant, linear, and quadratic terms of function f?

Solution

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$f(x)=(2x-3)(2x+3)$

Use the formula for the difference-of-squares:

$a^2-b^2=(a-b)(a+b)$

$\Rightarrow f(x)=(2x)^2-3^2$

$\Rightarrow f(x)=4x^2-9$

The constant term of function $f$ is $-9$, the linear term of function $f$ is $0$ (since we do not have term in the form $ax$ for any number $a$), and the quadratic term of function $f$ is $4x^2$.

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