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Mastering Factorization and Expansion of Quadratic Expressions in Algebra

This resource guides learners through the process of factorizing and expanding quadratic expressions. It includes step-by-step examples, such as manipulating expressions like ( x^2 + 6x + 8 ) into factors ( (x + 2)(x + 4) ), as well as expanding brackets for polynomial expressions. Practice problems bolster understanding of the material, with thorough solutions provided. Ideal for reinforcing knowledge in preparation for exams or enhancing skills in algebra for students.

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Mastering Factorization and Expansion of Quadratic Expressions in Algebra

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  1. Beginning factorising x2 + 6x + 8 = (x + 2)(x + 4) x2 + 2x 3 = (x + 3)(x  1)

  2. 10 mins: Expand the following brackets and simplify: 9x2 + 27x + 14 12x2 + 51x + 45 • (3x + 7)(3x + 2) • (4x + 5)(3x +9) • (5x + 4)(3x – 2) • (4x + 5)(2x – 4) • (7x – 2)(3x + 6) • (5x – 3)(2x – 6) • (8x – 2)(7x – 4) • (3x + 2)2 • (4x – 3)2 • (5x – 4)2 15x2 + 2x 8 8x26x 20 21x2+ 36x 12 10x2 36x+ 18 56x2 46x+ 8 9x2 + 12x+ 4 16x2 24x+ 9 25x2 40x+ 16

  3. 5 mins: Complete the following statements. 3 3 • (x + 2)(x + ……) = x2 + 5x + 6 • (x + 1)(x + ……) = x2 + 4x + 3 • (x + 5)(x + ……) = x2 + 9x + 20 • (x + 4)(x + ……) = x2 + 7x + 12 • (x + 2)(x + ……) = x2 + 4x + 4 • (x – 1)(x + ……) = x2 + 4x – 5 • (x – 2)(x + ……) = x2 + 3x – 10 • (x – 4)(x + ……) = x2 – x – 12 • (x – 3)(x – ……) = x2 – 5x + 6 • (x + 3)(x – ……) = x2 – 6x – 27 4 3 2 5 5 3 2 9

  4. 5 mins: Complete the following statements. 1 4 1 5 • x2 + 5x + 4 = (x + ……)(x + ……) • x2 + 6x + 5 = (x + ……)(x + ……) • x2 + 7x + 12 = (x + ……)(x + ……) • x2 + 7x + 10 = (x + ……)(x + ……) • x2 + 8x + 15 = (x + ……)(x + ……) • x2 + 11x + 30 = (x + ……)(x + ……) • x2 + x 6 = (x + ……)(x ……) • x2 + 2x 3 = (x + ……)(x ……) • x2x 6 = (x + ……)(x ……) • x2 7x + 12 = (x ……)(x ……) 3 4 2 5 3 5 5 6 3 2 3 1 2 3 3 4

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