Question

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

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

b) \\(2e(e + 3) - \frac{1}{3}(6e^2 + 9e - 12)\\)

Explanation:

Simplify the first term of part a

Using the Distributive Property knowledge point

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

Simplify the second term of part a

Using the Polynomial Division by Monomial knowledge point

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

Combine terms for part a

Using the Combining Like Terms knowledge point

$$
LATEXBLOCK0
$$

Expand the terms in part b

Using the Monomial Multiplication and Distributive Property knowledge points

$$
LATEXBLOCK1
$$

Combine terms for part b

Using the Combining Like Terms knowledge point

$$ (2e^2 + 6e) + (-2e^2 - 3e + 4) = 3e + 4 $$

Answer:

Question a

\(4a + 9b - 20\)

Question b

\(3e + 4\)