Difference of Two Squares and Perfect Square Trinomials · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Difference of Two Squares and Perfect Square Trinomials

Mathematics · Algebra · ages 14-15
Name ______________________   Date ____________

  1. (x + 8)(x - 8) expands to x squared - 64.

    Circle one:   True   False

  2. Which of these is a difference of two squares?

    • x squared - 4
    • x squared + 4
    • x squared - 3

  3. Which of these is a perfect square trinomial?

    • x squared + 6x + 9
    • x squared + 6x + 6
    • x squared + 3x + 9

  4. Factorise 16x squared - 9.

    • (16x + 9)(16x - 9)
    • (4x + 3)(4x - 3)
    • (4x + 9)(4x - 3)

  5. Use a difference of two squares to work out 61 times 59.

    Answer: ______________

  6. x squared + 12x + 36 is a perfect square trinomial, (x + a) squared. What is a?

    Answer: ______________

  7. Factorise 25x squared - 49.

    • (25x + 7)(25x - 7)
    • (5x + 49)(5x - 49)
    • (5x + 7)(5x - 7)

  8. Factorise x squared + 16x + 64.

    • (x + 16) squared
    • (x + 8) squared
    • (x + 4) squared

  9. Is the identity a squared - b squared = (a - b) squared always true?

    • No, (a - b) squared expands to a squared - 2ab + b squared
    • Yes, the middle terms always cancel
    • Only when b is zero

  10. Use a difference of two squares to work out 98 times 102.

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Difference of Two Squares and Perfect Square Trinomials W1-mt_GSpsHuserT-s1

  1. True · The middle terms -8x and +8x cancel, and 8 times -8 gives -64.
  2. x squared - 4 · x squared - 4 has two perfect squares joined by a minus. The others fail one of the three conditions.
  3. x squared + 6x + 9 · Halve the middle of x squared + 6x + 9 to get 3, and 3 squared is 9, so it is (x + 3) squared.
  4. (4x + 3)(4x - 3) · 16x squared is (4x) squared and 9 is 3 squared, so the brackets are (4x + 3)(4x - 3).
  5. 3599 · 61 times 59 = (60 + 1)(60 - 1) = 60 squared - 1 squared = 3600 - 1 = 3599.
  6. 6 · Halve the middle coefficient: 12 over 2 gives 6, and 6 squared is 36, so a = 6.
  7. (5x + 7)(5x - 7) · 25x squared is (5x) squared and 49 is 7 squared, so the brackets are (5x + 7)(5x - 7).
  8. (x + 8) squared · Halve the middle: 16 over 2 gives 8, and 8 squared is 64, so it is (x + 8) squared.
  9. No, (a - b) squared expands to a squared - 2ab + b squared · A squared bracket keeps a middle term, so (a - b) squared is a squared - 2ab + b squared, not a squared - b squared.
  10. 9996 · 98 times 102 = (100 - 2)(100 + 2) = 100 squared - 2 squared = 10000 - 4 = 9996.
Worksheet · LightMySky