Difference of Two Squares

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Use (a + b)(a − b) = a2 − b2

  1. Expand and simplify: (x + 5)(x − 5)

    Reveal answer 1

    x2 − 25

    The middle terms −5x and +5x cancel.

  2. Expand and simplify: (2x + 3y)(2x − 3y)

    Reveal answer 2

    4x2 − 9y2

    Square each complete term: (2x)2 = 4x2 and (3y)2 = 9y2

  3. Factorise completely: 3x2 − 27

    Reveal answer 3

    3(x − 3)(x + 3)

    Take out 3 first: 3(x2 − 9). Then use the difference of two squares.

  4. Calculate using the identity: 103 × 97

    Reveal answer 4

    (100 + 3)(100 − 3) = 10000 − 9 = 9991

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