Expanding Double Brackets · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Expanding Double Brackets

Mathematics · Algebra · ages 13-14
Name ______________________   Date ____________

  1. Expanding (x + 7)² gives x² + 49.

    Circle one:   True   False

  2. In FOIL, what does the letter O stand for?

    • Outer
    • Opposite
    • Over

  3. When you expand two brackets, you only need to multiply the first terms together.

    Circle one:   True   False

  4. When expanding (x + 1)(x + 2), what is the First term product?

    • x squared
    • 2x
    • 2, from 1 times 2

  5. A square garden has sides x metres long. One pair of sides is made 5 m longer and the other pair 1 m shorter. Which expression gives the new area in square metres?

    • x² + 4x - 5
    • x² - 5
    • x² + 6x - 5
    • x² + 4x + 5

  6. Expand (x - 3)(x + 6) and simplify.

    • x squared - 3x - 18
    • x squared + 9x - 18
    • x squared + 3x - 18

  7. Expand (x + 3)(x + 4) and collect like terms.

    • x squared + 7x + 12
    • x squared + 12x + 7
    • x squared + x + 12

  8. Simplify (x + 5)² - (x - 5)².

    • 10x
    • 0
    • 20x
    • 2x² + 50

  9. Expand and simplify (3x + 2)(x + 4).

    • 3x² + 12x + 8
    • 3x² + 14x + 8
    • 4x² + 14x + 8
    • 3x² + 6x + 8

  10. Priya expanded (x + 5)(x - 2) and wrote the final answer as x squared + 3x - 7. What mistake did she likely make?

    • She forgot the First term, x squared
    • Her Last term is wrong: 5 times -2 is -10
    • She added the Outer and Inner terms wrong
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Answer key

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

Expanding Double Brackets W1-mt_KhS7K1Mgrw-s1

  1. False · A squared bracket always produces a middle term from the two outside and inside products.
  2. Outer · O stands for Outer, the outside pair of terms in the two brackets.
  3. False · Every term in the first bracket must multiply every term in the second bracket, not just the first ones.
  4. x squared · F multiplies the first terms of each bracket: x times x makes x squared, not just x.
  5. x² + 4x - 5 · The new sides are x + 5 and x - 1, and (x + 5)(x - 1) = x² + 4x - 5.
  6. x squared + 3x - 18 · O gives 6x and I gives -3x. Collecting 6x - 3x makes 3x, so the answer is x squared + 3x - 18.
  7. x squared + 7x + 12 · F gives x squared, O gives 4x, I gives 3x, L gives 12. Collecting 4x + 3x makes 7x, so the answer is x squared + 7x + 12.
  8. 20x · Squaring a bracket with a minus sign inside flips the middle term, and that is what makes most of the answer cancel.
  9. 3x² + 14x + 8 · The four products are 3x², 12x, 2x and 8, and 12x + 2x = 14x.
  10. Her Last term is wrong: 5 times -2 is -10 · The x term, 3x, is correct. But 5 times -2 equals -10, so the constant should be -10, not -7.
Worksheet · LightMySky