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Lesson 14 of 15

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Ten questions, one for each idea. Read the table first.

Ten moves you may make on an expression without changing what it means
MoveHow it goes
Split a termCoefficient in front, then a letter part if there are letters.
Join same kindsAdd the coefficients. The letter part does not change.
Term times termMultiply coefficients, write letters side by side.
Into a bracketThe term outside reaches every term inside.
Bracket times bracketEvery term of one meets every term of the other.
Square a suma² + 2ab + b². The two rectangles are real pieces.
Difference of squares(a + b)(a − b) = a² − b².
Take a factor outDivide by what every term shares. Write it outside.
Put a number inWork both forms out and compare.
A trick as a lineName the number. Write each step. Join like terms.

What is the coefficient of the term −7m?

  • 7, because a coefficient counts how many there are
  • −7
  • `m`, because that is the part that varies

Four dates in a calendar square add to 4a + 16. What is the sum when a = 12?

  • 28, because only one `a` is counted
  • 64
  • 112, because `4a + 16` is read as `4(a + 16)`

What does 4b × 5b come to?

  • `20b`, because the two letters gather into one
  • `20b²`
  • `9b²`, because 4 and 5 are added

What does 3y(2y + 7) open out to?

  • `6y² + 7`, because only the first term inside is reached
  • `6y² + 21y`
  • `6y + 21y`, because `y × y` is written as `y`

What does (x + 4)(x + 6) come to?

  • `x² + 24`, because the firsts multiply and the lasts multiply
  • `x² + 10x + 24`
  • `x² + 10x`, because the last pairing carries no letter

A square is drawn on a side of 8 + 1. What is its area?

  • 65, which is 64 and 1
  • 81
  • 18, because the two parts are added and then doubled

What is the quickest route to 101 × 99?

  • Square 100 and add 1, giving 10,001
  • Read it as `(100 + 1)(100 − 1)`, giving 10,000 − 1
  • Read it as `(100 + 1)²`, giving 10,000 + 200 + 1

What is the largest thing that can be taken out of 9t² + 15t?

  • 3, because the letters are not the same in both terms
  • `3t`
  • `9t`, because 9 is the larger coefficient

You open an expression out. Both forms give 9 when the letter is 3. What has that shown?

  • That the opened form is correct
  • Not much yet, because two different forms can meet at one value
  • That the opened form is wrong, since one test proves nothing

Think of a number x. Multiply by 5. Add 15. Divide by 5. Take away x. What is left?

  • `x + 3`, because the number is not taken away
  • 3
  • 15, because 15 was added

Your book calls this Part II, Chapter 6. Its name is Algebra Play. Use the checking habit there.

Next: Area. It measures shapes, and it asks which length is the real height.

Reveal every answer to finish this lesson.