How do I factor this problem? 14x^2-56

Expert Answers

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You need to decompose the coefficients such that:

`14 = 1*2*7`

`56 = 1*2^3*7`

You need to write the expression using the factored form of coefficients, such that:

`2*7x^2 - 2^3*7`

You should notice that there exists the common factor `2*7` , hence, you may factor out `2*7` , such that:

`2*7(x^2 - 2^2)`

You need to convert the difference of squares `x^2 - 2^2` into a product, using the following formula, such that:

`a^2 - b^2 = (a-b)(a+b)`

Reasoning by analogy yields:

`x^2 - 2^2 = (x - 2)(x + 2)`

Hence, evaluating the factored form of the given expression, yields `14x^2 - 56 = 14(x - 2)(x + 2).`

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First factor out the gcf (greatest common factor) which is 14:

14x^2 - 56 = 14(x^2 - 4) 

We use the Difference of Two Squares Formula, for x^2 - 4: 

a^2 - b^2 = (a - b)(a + b)

So, 

x^2 - 4 = (x - 2)(x + 2)

We will now have,

14x^2 - 56 = 14(x^2 - 4) = 14(x - 2)(x + 2)

Hence, factored form of 14x^2 - 56 = 14(x - 2)(x + 2).

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