To factor the given expression, we will first identify and factor out the greatest common factor. Then, we will use the formula for the difference of two squares.
Factor Out the GCF
The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 5.
Recall the formula to factor a difference of squares.
a^2- b^2 ⇔ ( a+ b)( a- b)
We can apply this formula to our expression.
5 ( ( 2r^2)^2-( 3n^2)^2 )
⇕
5( 2r^2+ 3n^2)( 2r^2- 3n^2)
Checking Our Answer
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We can apply the Distributive Property and compare the result with the given expression.
After applying the Distributive Property and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!
