Answer:
3[a + b][a - b]
Step-by-step explanation:
Let us recall a useful formula. This formula can factorize any subtraction between perfect squares. The formula is known as a² - b² = (a - b)(a + b).
Let's apply the formula in the given expression as we can see that two perfect squares are being subtracted from each other. Then, we get:
[tex]\implies (2a - b)^{2} - (a - 2b)^{2}[/tex]
[tex]\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)][/tex]
Since the expression(s) inside the parentheses ( ) cannot be simplified further, we can open the parentheses ( ). Then, we get:
[tex]\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)][/tex]
[tex]\implies [2a - b - a + 2b][2a - b + a - 2b][/tex]
Now, we can combine like terms and simplify:
[tex]\implies [2a - b - a + 2b][2a - b + a - 2b][/tex]
[tex]\implies [a + b][3a - 3b][/tex]
Three is common in 3a - 3b. Thus, we can factor 3 out of the expression:
[tex]\implies [a + b][3a - 3b][/tex]
[tex]\implies [a + b] \times [3a - 3b][/tex]
[tex]\implies [a + b] \times 3[a - b][/tex]
[tex]\implies \boxed{3[a + b][a - b]}[/tex]
Therefore, 3[a + b][a - b] is the factorized expression of (2a - b)² - (a - 2b)².
Learn more about factoring expressions: https://brainly.com/question/1599970
