Help with class question
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mmm4444bot
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If a polynomial is one square term subtracted from another square term, then it is a difference of two squares.
EG:
4x^2 - 121
This polynomial is a difference of squares because 4x^2 is a square term and 121 is a square term, and one of these square terms is being subtracted from the other.
4x^2 = (2x)^2
121 = 11^2
Hence, the factorization of 4x^2 - 121 is (2x + 11)(2x - 11).
Sometimes, a polynomial that is a difference of squares may not be given in the form above, so you may need to rearrange it first, to see the difference of squares.
EG:
-2(61 - 2x^2) + 1
This is the same polynomial in the first example; it's been manipulated to look different (i.e., the constant was split into a sum, and then the rest was factored). Simplify the expression, first.
Multiply (expand) the factored part, and then add the 1:
(-2)(61) + (-2)(-2x^2) + 1
-122 + 4x^2 + 1
4x^2 - 122 + 1
4x^2 - 121
Of course, if you're given the factored form of a difference of squares, then you recognize it because you've memorized that special form.
EG:
(9x - 13)(9x + 13) is the factored form of the difference of squares 81x^2 - 169 because it matches the special form (a + b)(a - b) = a^2 - b^2.
Do you have a specific exercise that you need help with?
Please show your work, or ask direct questions about those parts that you do not understand.
Cheers ~ Mark :cool:
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