# How do you simplify (6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)?

Dec 16, 2016

${x}^{3} + 6 {x}^{2} + 2 x + 13$

#### Explanation:

Write as:$\text{ } + 1 \left(6 {x}^{2} - 3 + 5 {x}^{3}\right) - 1 \left(4 {x}^{3} - 2 x - 16\right)$

The 1's in front of the brackets are not normally written.
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$\textcolor{b l u e}{\text{Multiply everything inside the left brackets by +1}}$

$6 {x}^{2} - 3 + 5 {x}^{3}$

Ordering these gives

$\textcolor{b l u e}{5 {x}^{3} + 6 {x}^{2} - 3}$

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$\textcolor{b l u e}{\text{Multiply everything inside the right brackets by -1}}$

$\textcolor{b l u e}{- 4 {x}^{3} + 2 x + 16}$
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$\textcolor{b l u e}{\text{Putting everything together}}$

$5 {x}^{3} + 6 {x}^{2} - 3 \text{ } - 4 {x}^{3} + 2 x + 16$

Collecting like terms:

$\left(5 {x}^{3} - 4 {x}^{3}\right) + 6 {x}^{2} + 2 x + \left(16 - 3\right)$

$\textcolor{b l u e}{{x}^{3} + 6 {x}^{2} + 2 x + 13}$