Difference+Of+Squares

Perfect squares are terms that have a regular square root. For example, 16x 2 is a perfect square because the square root of 16x 2 is 4x, because (4x)(4x) = 16x 2. When there are only two terms in a quadratic, and both are perfect squares separated by a subtraction sign, this is a difference of squares.

To factor a difference of squares, a 2 - b 2 = (a+b)(a-b) because when you foil, the middle terms cancel out.

Examples: So to factor the expression 64x 2 - 25, find the square root of each term and follow the pattern above. The square root of 64x 2 is 8x, and the square root of 25 is 5. So 64x 2 - 25 = (8x+5)(8x-5).

Ex. x 2 - 225 (x+15)(x-15)

Here is another example:

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