Question

1. add or subtract each of the following (2 marks)

a) \\(2(a + 5b - 8) - \frac{(8a - 4a^2 + 2ab)}{2a}\\)

Explanation:

Expand the first term

Using the Distributive Property knowledge point

$$ 2(a + 5b - 8) = 2a + 10b - 16 $$

Simplify the second term

Using the Polynomial Division by Monomial knowledge point

$$ \frac{8a - 4a^2 + 2ab}{2a} = \frac{8a}{2a} - \frac{4a^2}{2a} + \frac{2ab}{2a} = 4 - 2a + b $$

Set up the subtraction

Using the Polynomial Simplification knowledge point

$$ (2a + 10b - 16) - (4 - 2a + b) = 2a + 10b - 16 - 4 + 2a - b $$

Combine like terms

Using the Combining Like Terms knowledge point

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Answer:

\(4a + 9b - 20\)