mat052

TWO TERMS: DIFFERENCE OF SQUARES TO BE FACTORABLE AN EXPRESSION WITH TWO TERMS MUST BE ONE OF THE FOLLOWING:

PERFECT SQUARE - PERFECT SQUARE
PERFECT CUBE - PERFECT CUBE
PERFECT CUBE + PERFECT CUBE

In this course, we only deal with the difference between two squares. Recognizing terms that are perfect squares Numbers: The square root of the number must be rational. The square root will be a whole number, a fraction,or a decimal that is repeating or terminating.
Letters with exponents: The exponent of the letter must be even.
Letters and numbers: Both must be perfect squares.

64 is a perfect square since it's square root is 8.
1/4 is a perfect square since it's square root is 1/2.
x⁸ is a perfect square since 8 is even.
x⁹ is not a perfect square since 9 is not even.
9x⁴ is a perfect square. (It's square root is 3x²)
3x² is not a perfect square since 3 is not a perfect square.

Factoring the difference of two squares

If an expression is of the form perfect square - perfect square it will factor into two binomials that have the same terms but opposite signs between them.
To factor A² - B²the two binomials would be (A - B)(A + B)
The pattern will be the same for any perfect square minus perect square with the first positions being the square root of the first term and the second positions being the square root of the second term.
To factor 4x² - 9y² we will get (2x - 3y)(2x + 3y)