Which of the expression bellow can be factored using the different of square method 17x^2-23y^2

Which of the expression bellow can be factored using the different of square method 17x^2-23y^2

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  1. A. [tex]9x^2 - 16y^2[/tex] .

    Step-by-step explanation:

    A difference of squares problem is factored as :[tex]a^2 - b^2 = (a + b)(a - b)[/tex]For this both terms in the form of squares and a minus sign between them.

    From all the options only option A has both terms square and they minus sign between them.

    Also, [tex]9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)[/tex]

    Here a= 3x and b= 4

    Hence, the correct answer is A. [tex]9x^2 - 16y^2[/tex] .

  2. The difference of the squares method is a short-cut method that is expressed a2 - b2 = ( a + b ) *(a-b). In this case, a2 and b2 should be perfect squares in which a and b are the square roots. In this case, 100 and 49 are perfect squares, hence the answer is C. 

  3. 25x^2 - 64y^2

    The first thing you can do is look for a subtraction sign. The word difference implies subtraction, so you can rule out any expressions that add terms. Secondly, you can look for squares. 17x^2 - 23y^2 is a subtraction expression, but 17 and 23 are not squares. However, 25x^2 - 64x^2 is a subtraction expression and its terms are squares. 25 = 5x5, 64 = 8x8. Hope this helps!

  4. C

    Step-by-step explanation:

    A difference of squares can be factored in general as

    a² - b² = (a - b)(a + b)

    We are looking for 2 terms separated by a - and perfect squares on either side. The only one meeting this criteria is

    25x² - 64y²

    = (5x)² - (8y)²

    = (5x - 8y)(5x + 8y) ← in factored form

  5. The expression that can be factored using the difference of squares method:
    C) [tex]100x^{2}-49y^{2}[/tex]
    Factorization:
    [tex]100x^{2}-49y^{2} = (10x+7y)*(10x-7y)[/tex]

  6. Difference of squares method is a method that is used to evaluate the difference between two perfect squares.

    For example, given an algebraic expression in the form:
    [tex]x^2-y^2[/tex]
    can be factored as follows:
    [tex](x-y)(x+y)[/tex]

    From the given expressions, the only expression containing two perfect squares with the minus sign in the middle is the expression in option A.
    i.e. [tex]25x^2-64y^2[/tex]
    which can be factored as follows:
    [tex](5x-8y)(5x+8y)[/tex].

  7. Some examples of the difference of 2 squares are as ffoolows:-

    x^2 -  1

    36y^2 - 4x^2

    a^2 - b^2

    z^2 - 16

    Note each term is a perfect square and theres a negative sign in between them

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