How do you factor a difference of two squares? Is there a similar strategy for the sum of two squares? You can determine if it's a difference of two squares, by seeing if both terms are perfect squares, and can be written in the form a 2 - b 2.
Michael already showed how to factor it. The difference of two squares occurs when the middle term or "b" of your polynomial is absent. Notice how the signs alternate so that you are squaring the number by its positive and negative value. That means that when you multiply it out the cross product sum or middle term "b" has equal and opposite values and will then drop out of the expression.
The sum of two squares involves complex conjugates using the imaginary number or operator "i". Every complex number has a corresponding conjugate and exist in pairs, this is typically written as.
This matches the original, so we know we factored correctly. We take the square root of 4x 2 which is 2x and put that in the back of each.
When factoring polynomials, the first step is always to look for common factors and to factor them out. After that, you can see if the polynomial can be factored further. There is a special situation called the difference of two squares that has a special pattern for factoring. Here is the pattern: First, notice that there are three requirements that must be met in order for us to be able to use this pattern. Here's a couple examples: 1 First check for common factors - there are none, so we can continue on to check the criteria.
Final answer:. We can check this by multiplying it out remember to distribute or use FOIL. Final answer. There is a common factor of 3, so we must factor that out first.
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