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Definition. The difference of squares of two expressions is equal to product of sum of these expressions and the difference of these expressions:
a^{2}  b^{2} = (a + b)·(a  b) Derivation of the formula of difference of squaresThe proof of the formula is very simple. To prove the formula is sufficient to multiply the expression: (a  b)·(a + b) = a^{2} + ab  ba  b^{2} = a^{2}  b^{2}
Applying of difference of squares formula
Difference of squares formula convenient to use:
Examples of taskExample 1. Expand brackets (x  3)·(x + 3).
Solution: Apply the difference of squares the formula. (x  3)·(x + 3) = x^{2}  3^{2} = x^{2}  9
Example 2. Expand brackets (2x  3y^{2})·(2x + 3y^{2}).
Solution: Apply the difference of squares the formula. (2x  3y^{2})·(2x + 3y^{2}) = (2x)^{2}  (3y^{2})^{2} = 4x^{2}  9y^{4}
Example 3. Simplify the expression Solution: Apply the difference of squares formula in numerator.
Factoring: Some special cases
Square of the sum
Square of the difference
Difference of squares
Cube of sum
Cube of difference
Sum of cubes
Difference of cubes
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