This is a free lesson from our course in Algebra I
In this part of lesson you'll learn how to factor a quadratic using the perfect square method. In such
cases, not only can the quadratic can be factored into two expressions, but the
expressions are the same.If we try to explain it in text, here is the general rule
if you have a quadratic equation in which first and last term are both perfect squares
and middle term is two times the square root of the first and last terms multiplied, it simplifies
the quadratic to a binomial product or just one binomial raised to the second
power. Reading this explanation in text is confusing to many of you --
just click on the video of our instructor explaining it above, and you'll understand
the concept much more easily. (More text below video...)
(Continued from above) Note that perfect
square trinomials are often expressions of one of the following
• (x2 + 2ax + a2), which is the same as
(x + a)2
• (x2 - 2ax + a2), which is the same as
(x - a)2
With x2 + 6x + 9, or any perfect square of form ax2
+ bx + c, look at the 'a' term and the 'c' term
to see if they are all squares. 1 and 9 both check out. Then set up an expression
like this (x + 3)(x + 3). We need to see that the 'b'
term comes out as 6, and therefore we should multiply again to check. The way we
simplified the quadratic to (x + 3)2 is that the first term
is the square route of 'a' and the later term is the square route of 'c'.
A square route of a number is the exact number that can be squared to give the original.
For example: the square route of 4, is 2 because 2 * 2 = 4 and 2 =2. Another type
of perfect square is where 'a' (the x2 coefficient)
is not 1. For example: 4x2 + 4x + 1 , the 'a'
term is a square and 'c' is a square so this is a perfect square quadratic.
There is one more thing to check, though. FOIL the two expressions and find if the
'b' term comes out right. So the expression is (2x + 1)2.
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