Question

Factor the following binomial.
81 - 36x²
([?] + [?]x) ([?] - [?]x)

Answer 1

Answer: If you use 9² - 36x², then you can factor it as (9 + 6x)(9 - 6x).

Explanation:

Edit: for a difference of two squares, use a² - b² = (a-b)(a+b). Since 9² = 81, use 9 for a, and 6 for b since 6² = 36.

If you take 9² - 36x², then you could write it as (9 + 6x)(9 - 6x).

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First, factor out a common term. 81 and 36 are both divisible by 9 since 9*9=81 and 9*4=36, so:

9(9 - 4x²)

Next, factor 9 - 4x². We know that 3² = 9 and 2x*(-2x)= - 4x². So, write this as (3+2x)(3-2x);

And finally,

9(3 + 2x)(3 - 2x).

81 - 36x² factored is 9(3 + 2x)(3 - 2x).