Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can use the distributive property to expand and factor expressions.
Key words
The Distributive Property — Multiply a factor by every term inside parentheses.
Distributive Property — Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.
Factor — A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
Expand — To multiply out the parentheses in an expression.
Equivalent — Expressions that always have the same value.
Coefficient — The number in front of a letter, like the 3 in 3x.
Like terms — Terms with the same letter raised to the same power, like 2x and 5x.
Steps
Each bundle has a ticket ($15) and a snack ($5). For 3 bundles I can write 3(15 + 5).
Way 1: add inside first. 15 + 5 = 20, then 3 × 20 = 60.
Way 2: distribute the 3 to each part. 3 × 15 + 3 × 5.
That is 45 + 15 = 60.
Both ways give $60, so 3(15 + 5) = 3 × 15 + 3 × 5.
Try it
Grandma packs 4 snack bags. Each bag has y grapes and 5 crackers, so the total is 4(y + 5). Which expression is equivalent to 4(y + 5)?
Check your answer
4y + 20
4(y + 5) = 4 × y + 4 × 5 = 4y + 20. The 4 must multiply BOTH terms — multiplying only the y gives 4y + 5, multiplying only the 5 gives y + 20, and adding 4 + 5 instead of multiplying gives 4y + 9.
Sentence starter
I know ___ because ___.
Goal: I can explain my steps using the words distributive property, factor, expand, and equivalent.