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Note 5: Expanding Two Brackets

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) . = y 2 - 6y + 4y - 24 = y 2 - 2y - 24. (2x - 7)(3x + 4) .

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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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