Freefall 8 notes:

Multiplying Algebraic Terms

We show multiplication between numbers and pronumerals as the number first then the letter.

For example, 2 × a = 2a, 5 × d = 5d and 4 × a × d = 4ad (or 4da).

When several numbers and letters are mixed up, calculate the product of the numbers first, then the letters. For example, 5e × 2g = 10eg. Note that when the same letter is featured twice a squared term will result. E.g. 3q × 5q = 15q2. A letter times itself is that letter squared.

(a × a = a^2, c × c = c^2 etc. )

When you multiply negative numbers .....

Negative × Positive = Negative (different signs = negative)

Positive × Negative = Negative (different signs = negative)

Negative × Negative = Positive (same signs = Positive)

Remember that three negatives swap the sign back to negative again.

Negative × Negative × Negative = Positive × Negative = Negative

Dividing Algebraic Terms

Division can be shown with a ‘÷’ or a vinculum. A vinculum is a horizontal line that separates the numerator (top part of a fraction) from the denominator (bottom part). So you have to know both ways that a division can be written.

Simplifying algebraic expressions means reducing the expression to its simplest form. You have to find the HCF (highest common factor) and divide both top and bottom numbers by the HCF. You don’t write ‘1’ except in the top line if there are no pronumerals in that line.