SAT Mathematics Practice Test 3

To rewrite the difference $\left(-3{\mathit{x}}^2+5\mathit{x}-2\right)-2\left({\mathit{x}}^2-2\mathit{x}-1\right)$ in the form $\mathit{a}{\mathit{x}}^2+\mathit{b}\mathit{x}+\mathit{c},$ the expression can be simplified by using the distributive property and combining like terms as follows:
$\left(-3{\mathit{x}}^2+5\mathit{x}-2\right)-\left(2{\mathit{x}}^2-4\mathit{x}-2\right)$
$\left(-3{\mathit{x}}^2-2{\mathit{x}}^2\right)+\left(5\mathit{x}-\left(-4\mathit{x}\right)\right)+\left(-2-\left(-2\right)\right)$
$-5{\mathit{x}}^2+9\mathit{x}+0$
Alternatively, since b is the coefficient of x in the difference $\left(-3\mathit{x}2+5\mathit{x}-2\right)-2\left({\mathit{x}}^2-2\mathit{x}-1\right)$, one need only compute the x-term in the difference.
The x-term is $5\mathit{x}-2\left(-2\mathit{x}\right)=5\mathit{x}+4\mathit{x}=9\mathit{x},$ so the value of b is 9.