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Example 1
$2x^3 -3x^2 - 2x -5$ subtracted from $-3x^2-5x+7$ is equal to
- $2x^3+3x-12$
- $-2x^3-3x+12$
- $2x^3 -6x^2 - 2x +2$
- $2x^3 -3x^2$
- $ 2x + 5$
Solution
This example is about subtracting polynomials.
- We first need to understand that "$A$ subtracted from $B$" is mathematically translated as $B - A$. Hence we are asked to simplify
$(-3x^2-5x+7)-(2x^3 -3x^2 - 2x -5)$
- We now need to rewrite the above expression without brackets. The first bracket has a $+1$ or just $1$ in front and nothing changes when you multiply an expression by $1$. The second bracket has a $-1$ in front and you need to multiply all terms by $-1$ in that expression (distributive property). Hence
$(-3x^2-5x+7)-(2x^3 -3x^2 - 2x -5)$
${\color{red}{1}}(-3x^2-5x+7){\color{red}{-1}}(2x^3 -3x^2 - 2x -5)$
$= -3x^2-5x+7-2x^3 +3x^2 + 2x +5$
- We now group like terms which are terms with the same variable to the same power. Hence
$=\color{red}{-2x^3}\color{blue}{-3x^2+3x^2}\color{green}{-5x+2x}\color{magenta}{+7+5}$
$=\color{red}{-2x^3}\color{green}{-3x}\color{magenta}{+12}$
Answer B
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