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Note 5: Expanding Two Brackets

Learn how to expand and simplify algebraic expressions by multiplying the terms in brackets and simplifying the result. Explore examples of expanding the difference of two squares and perfect squares. Practice exercises included.

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Note 5: Expanding Two Brackets

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  1. Note 5: Expanding Two Brackets To expand out two brackets: • Multiply the both parts of the first bracket with both parts of the second bracket • Simplify if possible Example: Expand and simplify the following (y + 4)(y – 6) = y2 - 6y + 4y - 24 = y2 - 2y - 24 (2x - 7)(3x + 4) = 6x2 + 8x – 21x - 28 = 6x2 - 13x - 28

  2. Difference of Two Squares The difference of two squares has two brackets the same except for the signs (+ or -), when expanded there will be no middle term. (a – b)(a + b) = a2 – b2 Example: Expand and simplify the following (x + 4)(x – 4) = x2 – 4x + 4x - 16 = x2 - 16 (3y - 2)(3y + 2) = 9y2 – 6y + 6y - 4 = 9y2 - 4

  3. Perfect Squares A perfect square has both brackets the same: (a – b)2 = (a – b)(a - b) = a2 – 2ab + b2 (a + b)2 = (a + b)(a + b) = a2 + 2ab + b2 Example: Expand and simplify the following (x + 7)2 = (x + 7)(x + 7) = x2 + 14x + 49 (4y - 5)2 = (4y - 5)(4y - 5) = 16y2 – 40y + 25

  4. Page 129 Exercise 4C – 4E

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