The polynomial below is a perfect square trinomial of the form a2 - 2ab + b2
1 answer:
This is a true statement. Here's how we know. The factors of that general formula are (ax - b)(ax - b). If that is in fact the general formula of the quadratic shown, then our a would be 2 and our b would be 3, since 2 times 2 is 4 which is the leading coefficient, and 3 times 3 is 9 which is the constant. Those factors, filled in accordingly, would be (2x - 3)(2x - 3). If we FOIL those out we should get back the quadratic in question. FOILing gives us
which of course simplifies to
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We have been given the expression
We have to write this expression in the form
In order to write the given expression in this form, we can use some exponent property.
On using the property (1), we have
Now, on using the property (2), we get
Therefore, the simplified form of the given expression is