factorise fully:18xsquared-50ysquared
To factorize the expression 18x^2 - 50y^2 fully, we need to look for common factors and use factoring techniques.
Step 1: Factor out the Greatest Common Factor (GCF)
The GCF of 18x^2 and 50y^2 is 2.
2(9x^2 - 25y^2)
Step 2: Recognize a Difference of Squares pattern
The expression 9x^2 - 25y^2 can be further factored using the difference of squares pattern. In this pattern, we have the form a^2 - b^2, which can be factored as (a + b)(a - b).
So, we have:
2(3x + 5y)(3x - 5y)
Therefore, the fully factorized form of 18x^2 - 50y^2 is 2(3x + 5y)(3x - 5y).