Factoring difference of squares: x2−y2x^2 - y^2

Factoring difference of squares: x2−y2x^2 - y^2

Basic concepts: Multiplying binomial by binomial, Factoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2, Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2),
Related concepts: Completing the square, Converting from general to vertex form by completing the square, Solving quadratic equations by factoring, Solving quadratic equations by completing the square,

Lessons

  • Introduction
    What is a “difference of squares”?
  • 1.
    Factor:
    a)
    x2−49{x^2} - 49

    b)
    4x2+254{x^2} + 25

    c)
    16−9x216 - 9{x^2}

  • 2.
    Factor:
    a)
    100x2−49y2100{x^2} - 49{y^2}

    b)
    32x2−242y232{x^2} - 242{y^2}

    c)
    2a3b−8ab32{a^3}b - 8a{b^3}

    d)
    25a2b2−4c225{a^2}{b^2} - 4{c^2}

  • 3.
    Factor:
    a)
    (x−y)2−(z)2{\left( {x - y} \right)^2} - {\left( z \right)^2}

    b)
    (5a+6b)2−(9a−b)2{\left( {5a + 6b} \right)^2} - {\left( {9a - b} \right)^2}

    c)
    169(x−3)2−25(x+6)2169{\left( {x - 3} \right)^2} - 25{\left( {x + 6} \right)^2}

  • 4.
    Factoring “difference of squares” more than once

    Factor:
    a)
    x4−16{x^4} - 16

    b)
    162a4−2b4162{a^4} - 2{b^4}

    c)
    5a7b8−80a3c45{a^7}{b^8} - 80{a^3}{c^4}

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19.
Quadratic Functions
19.1
Factorise by taking out the greatest common factor
19.2
Factorise by grouping
19.3
Factorising perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2
19.4
Factorising difference of squares: x2−y2x^2 - y^2
19.5
Factorising trinomials
19.6
Solving polynomials with unknown coefficients
19.7
Solving polynomials with unknown constant terms
19.8
Properties and graphs of quadratic functions
GCE N(A)-Level Maths
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