factorise the following 2a² - 2b² - 3a - 5b - 2
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factorise the following 2a² - 2b² - 3a - 5b - 2
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Answer:
To factorize the expression 2a² - 2b² - 3a - 5b - 2, you can look for common factors and use techniques like grouping. Here's how you can factorize it:
2a² - 2b² - 3a - 5b - 2
First, group the terms:
(2a² - 2b²) - (3a + 5b) - 2
Now, factor each group separately:
2(a² - b²) - (3a + 5b) - 2
Use the difference of squares identity a² - b² = (a + b)(a - b):
2[(a + b)(a - b)] - (3a + 5b) - 2
Now, distribute the 2 into the brackets:
2a(a + b) - 2b(a + b) - (3a + 5b) - 2
Now you can see that you have a common factor of (a + b):
(2a - 2b)(a + b) - (3a + 5b) - 2
Factor out (a + b) from the first two terms:
2(a - b)(a + b) - (3a + 5b) - 2
Now, you have two binomials, (a - b) and (a + b). The expression is fully factorized as:
2(a - b)(a + b) - (3a + 5b) - 2