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:
$3\text{x}^2+5\text{x}-7\\\underline{\ \ \ \ \ \ \times (\text{x}-1)\ \ }\\3\text{x}^3+5\text{x}^2-7\text{x}\\ \underline{\ \ \ \ \ \ -3\text{x}^2 -5\text{x}+7\ }\\3\text{x}^3+2\text{x}^2-12\text{x}+7$
$\left(x^2-3 x+3\right)(x+4)$
By column method:
$\text{x}^2-2\text{x}+3\\ \underline{\ \ \ \ \times(\text{x}+4)\ \ \ }\\\text{x}^3-2\text{x}^2+3\text{x}\\\underline{\ \ \ \ \ \ \ \ \ 4\text{x}^2-8\text{x}+12}\\\text{x}^3+2\text{x}^2-5\text{x}+12$
$\left(3 x^2+5 x-7\right)(x-1)-\left(x^2-2 x+3\right)(x+4)$
$=3 x^3+2 x^2-12 x+7-\left(x^3+2 x^2-5 x+12\right)$
$=3 x^3-x^3+2 x^2-2 x^2-12 x+5 x+7-12$
$=2 x^3-7 x-5$
By column method:
$3\text{x}^2+5\text{x}-7\\\underline{\ \ \ \ \ \ \times (\text{x}-1)\ \ }\\3\text{x}^3+5\text{x}^2-7\text{x}\\ \underline{\ \ \ \ \ \ -3\text{x}^2 -5\text{x}+7\ }\\3\text{x}^3+2\text{x}^2-12\text{x}+7$
$\left(x^2-3 x+3\right)(x+4)$
By column method:
$\text{x}^2-2\text{x}+3\\ \underline{\ \ \ \ \times(\text{x}+4)\ \ \ }\\\text{x}^3-2\text{x}^2+3\text{x}\\\underline{\ \ \ \ \ \ \ \ \ 4\text{x}^2-8\text{x}+12}\\\text{x}^3+2\text{x}^2-5\text{x}+12$
$\left(3 x^2+5 x-7\right)(x-1)-\left(x^2-2 x+3\right)(x+4)$
$=3 x^3+2 x^2-12 x+7-\left(x^3+2 x^2-5 x+12\right)$
$=3 x^3-x^3+2 x^2-2 x^2-12 x+5 x+7-12$
$=2 x^3-7 x-5$
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$VI$
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