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20 February, 21:06

What is the expression in factored form? 9x^2 - 12x + 4

A. (3x + 2) ^2

B. (-3x-2) ^2

C. (3x-2) ^2

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

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Answers (2)
  1. 20 February, 21:35
    0
    The answer is (3x-2) ^2
  2. 20 February, 21:36
    0
    C. (3x - 2) ²

    Step-by-step explanation:

    The square of a binomial can be written as (a + b) ². If you expand this formula, you get

    (a + b) (a + b). Use F. O. I. L. to multiply this out ...

    F - stands for 'Firsts' (the first values in each set of parenthesis)

    O - stands for 'Outsides' (the first value in the first set of parenthesis, and the

    second value in the second set of parenthesis)

    I - stands for 'Insides' (the second value in the first set of parenthesis, and

    the first value in the second set of parenthesis)

    L - stands for 'Lasts' (the second value in each set of parenthesis)

    This is the order you multiply them in ... so we get

    F - a² (a times a)

    O - ab

    I - ba (which we rewrite as ab, since order doesn't matter when multiplying)

    L - b²

    We add them together to get a² + ab + ab + b²

    which simplifies to a² + 2ab + b²

    Read this as, the square of the first term in the parenthesis (a²), plus twice the product of the terms (2ab is twice the product of a and b), plus the square of the last term in the parenthesis)

    So to solve this we need to factor 9x² - 12x + 4

    Look at the bold paragraph above and work backwards.

    Take the square root of the term 9x², which is 3x. That goes in the first value of the parenthesis, so we have

    (3x + b) ²

    We know that - 12x is twice the product of the two terms, so we divide by 2 to see the product of the two terms.

    -12x/2 = - 6x,

    We know one term, so divide - 6x by the first term, 3x, to find the second term.

    -6x/3x = - 2

    So the last term in our set of parenthesis is - 2, so we have

    (3x - 2) ²
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