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← We Distribute, Yet Things Multiply

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Lesson 10 of 11

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Eight ideas, eight checks. Read the table first.

Eight ways a bracket opens, and what has to survive it
IdeaHow it goes
A free cutA cut never changes the total. 160 + 40 = 200.
Over a sumThe outside number meets every term. 8 × (20+5) = 160+40.
With a letter3(n + 4) is 3n + 12, at every value of n.
Over a subtractionEach term keeps its own sign. 7 × (30−2) = 210 − 14.
Two bracketsEvery term meets every term: four products.
CollectingOnly matching letter parts gather. 3x + 2x = 5x.
Squaring a sumFour pieces, two of them alike: a² + 2ab + b².
A chosen cutCut at a round number. 23 × 7 = 140 + 21.

A hall has 8 rows of 25 chairs. Every row is split after the 13th chair. What do the two sides hold?

  • 104 and 96, adding to 200
  • 104 and 96, adding to 208
  • 13 and 12, the two row lengths

Eight kits, each holding a ₹20 notebook and a ₹5 pen. Which line gives the bill?

  • 8 × 20 + 8 × 5, which is ₹200
  • 8 × 20 + 5, which is ₹165
  • 8 × 20 × 5, which is ₹800

3(n + 2) and 5n both give 15 at n = 3. Are they the same expression?

  • No — at `n` = 4 they give 18 and 20
  • Yes, since they agree at `n` = 3
  • Yes, both are built from a 3 and a 5

What does 7 × (30 − 2) come to?

  • 210 − 14, which is 196
  • 210 − 2, which is 208
  • 210 + 14, which is 224

What does (x + 2)(x + 3) expand and collect to?

  • `x² + 5x + 6`
  • `x² + 6`, from firsts and lasts alone
  • `x² + 5x`, since both numbers are used up

Which of these gathers into a single term?

  • `2x + 3x`, since both letter parts are `x`
  • `x² + 5x`, since both have an `x`
  • `4x + 7`, since 4 and 7 are numbers

A square patch has a side of 3 + 4 tiles. What does the patch really hold?

  • 25 tiles, from `3² + 4²`
  • 49 tiles
  • 12 tiles, from 3 × 4

What is the quickest way to work out 6 × 104?

  • 6 × 100 + 6 × 4, which is 600 + 24
  • 6 × 100 × 4, treating 104 as 100 and 4
  • 6 × 100 + 4, since the 4 is small

Your book calls this Part I, Chapter 6. Its name is We Distribute, Yet Things Multiply. Use these habits there.

Next: Proportional Reasoning-1. It compares amounts, as you meet them every day.

Reveal every answer to finish this lesson.