# What is the standard form of f(x)=(x-1)^2-(3x+4)^2 ?

Mar 8, 2016

Standard form is $f \left(x\right) = - 8 {x}^{2} - 26 x - 15$

#### Explanation:

Standard form of quadratic polynomial with one variable is $f \left(x\right) = a {x}^{2} + b x + c$.

Hence to convert f(x)=(x−1)^2−(3x+4)^2, one should expand the RHS, using identity ${\left(a \pm b\right)}^{2} - {a}^{2} \pm 2 a b + {b}^{2}$

f(x)=(x−1)^2−(3x+4)^2

= ${x}^{2} - 2 x + 1 - \left({\left(3 x\right)}^{2} + 2 \times 3 x \times 4 + {4}^{2}\right)$ or

= ${x}^{2} - 2 x + 1 - \left(9 {x}^{2} + 24 x + 16\right)$

= ${x}^{2} - 2 x + 1 - 9 {x}^{2} - 24 x - 16$

= $- 8 {x}^{2} - 26 x - 15$