Question
Simplify:
$\left(3 x^2+5 x-7\right)(x-1)-\left(x^2-3 x+3\right)(x+4)$
$\left(3 x^2+5 x-7\right)(x-1)-\left(x^2-3 x+3\right)(x+4)$
✓
Answer
$\left(3 x^2+5 x-7\right)(x-1)$
By column method:
$3 x^2+5 x-7$
$\quad \times(x-1)$
$\frac{x(x-1)}{3 x^3+5 x^2-7 x}$
$\frac{-3 x^2-5 x+7}{3 x^3+2 x^2-12 x+7}$
$\left(x^2-3 x+3\right)(x+4)$
By column method:
$x^2-2 x+3$
$\times(x+4)$
$x^3-2 x^2+3 x$
$\frac{4 x^2-8 x+12}{x^3+2 x^2-5 x+12}$
$\left(3 x^2+5 x-7\right)(x-1)-\left(x^2-2 x+3\right)(x+4)$
$=3 x^3+2 x^2-12 x+7-\left(x^3+2 x^2-5 x+12\right)$
$=3 x^3-x^3+2 x^2-2 x^2-12 x+5 x+7-12$
$=2 x^3-7 x-5$
By column method:
$3 x^2+5 x-7$
$\quad \times(x-1)$
$\frac{x(x-1)}{3 x^3+5 x^2-7 x}$
$\frac{-3 x^2-5 x+7}{3 x^3+2 x^2-12 x+7}$
$\left(x^2-3 x+3\right)(x+4)$
By column method:
$x^2-2 x+3$
$\times(x+4)$
$x^3-2 x^2+3 x$
$\frac{4 x^2-8 x+12}{x^3+2 x^2-5 x+12}$
$\left(3 x^2+5 x-7\right)(x-1)-\left(x^2-2 x+3\right)(x+4)$
$=3 x^3+2 x^2-12 x+7-\left(x^3+2 x^2-5 x+12\right)$
$=3 x^3-x^3+2 x^2-2 x^2-12 x+5 x+7-12$
$=2 x^3-7 x-5$
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