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31 January, 17:06

Replace ∗ with a monomial so that the derived expression may be represented as a square of a binomial: * -42pq+49q^2

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  1. 31 January, 20:34
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    36p²

    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 know what makes * -42pq+49q^2 factor into some form of (a + b) ².

    Look at the bold paragraph above and work backwards.

    Take the square root of the term 49q², which is 7q. That goes in the second value of the parenthesis, so we have

    (c - 7q) ² (there is a subtraction sign because it's - 42pq)

    We know that 42pq is twice the product of the two terms, so we divide by 2 to see the product of the two terms.

    42pq/2 = 42pq,

    We know one term, so divide 42pq by the second term, 7q to find the first term.

    42pq/7q = - 6p

    So the first term in our set of parenthesis is - 6p, so we have

    (6p - 7q) ²

    To get the missing value, square the first term, (6p) ² = 36p²

    So 36p² is our missing term.

    16x^2+24xy + 9y² = (4x + 3y) ²
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