The Distributive Property Guided Notes + Homework Set

State and apply the rule that a term outside a parenthesis multiplies every term inside it

Distribute a negative multiplier correctly, treating each term inside as positive or negative before multiplying

Distribute a bare negative sign, as in –(12 – 4x + 5y), where the multiplier is an unwritten -1

Combine like terms after distributing, so 3(x – 6) + 5 is simplified rather than left expanded

Identify which number is being distributed when the parenthesis appears in the middle of an expression rather than at the start

Work the notes in printed order: positives, then negatives, then combining like terms, then parentheses that are not at the front — each block adds exactly one new difficulty

The bare-negative cases, –(19a – 8 + 11c – 12k) on the notes and –(12 – 4x + 5y) on the assignment, are where most errors start; the notes give the sign rule immediately before them

Question 8 on the assignment, -23 + 5(-2x + 6) + 10x, is the one that tests all three skills at once — distributing, handling the negative constant, and combining like terms

The notes sheet and the assignment can be split across two days: the notes carry the worked build-up, and the assignment repeats the same four difficulty steps without support

Several assignment questions use uncommon variables — w, c, f, h — so students who have only ever seen x need a word about that before they start

Applying the distributive property — students complete the rule in the notes and then expand expressions from 7(y + 6) to 8(3x – 2 + w).

Distributing negatives — six notes expressions and several assignment questions put a negative outside the parenthesis, as in -9(-9 + 8f) and -5(4 – 10x).

Handling an implicit -1 — expressions written as –(12 – 4x + 5y) require students to recognise the unwritten multiplier.

Combining like terms after expanding — 6(2c – 1) – 10 + 3c and -4y + 8x – 7(x – 4y) are only finished once the expansion is collected.

Locating the distributed term — a block of expressions puts the parenthesis mid-expression, so students must decide what is being distributed before multiplying.