Algebra I: Factoring a quadratic using the perfect square method
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...)
<h2> Factoring a quadratic using the perfect square method - Watch video (Algebra I)</h2> <p> factoring, quadratic, factor, expression, term, rule, perfect square, trinomials, square root, online math, power, factoring trinomials, binomial, trinomial, product, algebra online, practice questions, solution</p> <p> If we 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.</p>
Other useful lessons:
Factoring an expression of exponents with the same base
Factoring a quadratic into binomials
Factoring a 3rd degree polynomial
(Continued from above) Note that perfect square trinomials are often expressions of one of the following forms:
• (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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