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

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

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] .

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.

C

Step-by-step explanation:

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!

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

100x2 - 49y2 is the answer

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]

It would be D because both are positive and are square roots

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].

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