Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)

Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)

The word "difference" in the difference of squares essentially means "subtract". However, solving this type of question is not subtracting the squared terms. It involves factoring and multiplying conjugates, which you will learn it all in this lesson.
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
Related Concepts: Factor by taking out the greatest common factor, Factor by grouping, Factoring difference of squares: x2−y2x^2 - y^2, Factoring trinomials

Lessons

  • 1.
    Find the difference of squares
    a)
    (3x+4y)(3x−4y)(3x + 4y)(3x - 4y)

    b)
    (−x2−3y2)(−x2+3y2)(-x^2-3y^2)(-x^2+3y^2)

    c)
    x2−25x^2 - 25

    d)
    16−25x416 - 25x^4

    e)
    16x2y8−416x^2y^8 - 4

    f)
    x2n−25x^{2n} - 25

    g)
    x8−1x^8 - 1

    h)
    (x2+6x+9)−4y2(x^2 + 6x + 9) - 4y^2

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17.
Factorising Polynomial Expressions
17.1
Common factors of polynomials
17.2
Factorising polynomials by grouping
17.3
Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
17.4
Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
17.5
Factorising polynomials: x2+bx+cx^2 + bx + c
17.6
Applications of polynomials: x2+bx+cx^2 + bx + c
17.7
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
17.8
Factorising polynomials: ax2+bx+cax^2 + bx + c
17.9
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
17.10
Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
17.11
Evaluating polynomials
17.12
Using algebra tiles to factorise polynomials
17.13
Solving polynomial equations
17.14
Word problems of polynomials
AU Year 10 Maths
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