Question

Factorize:(2a - b)² - (a - 2b)²​

Answer 1

Answer:

3(a - b)(a + b)

Step-by-step explanation:

Factorize: (2a - b)² - (a - 2b)²​

• Different of Perfect a Square rule: a²​ - b²​ = (a + b)(a - b)

(2a - b)² - (a - 2b)²​ = [(2a - b) + (a - 2b)] × [(2a - b) - (a - 2b)]

1. Distribute and Simplify:

Distribute the (+) sign on the first bracket and simplify: [(2a - b) + (a - 2b)] → 2a - b + a - 2b → (3a - 3b)

Distribute the (-) sign on the first bracket and simplify: [(2a - b) - (a - 2b)] → 2a - b – a + 2b → (a + b)

We now have:

(3a - 3b)(a + b)

2. Factor out the Greatest Common Factor (3) from 3a - 3b:

(3a - 3b) → 3(a - b)

3. Add "(a + b)" back into your factored expression:

3(a - b)(a + b)

Hope this helps!

Answer 2

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:

$\implies (2a - b)^{2} - (a - 2b)^{2}$

$\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]$

Since the expression(s) inside the parentheses ( ) cannot be simplified further, we can open the parentheses ( ). Then, we get:

$\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]$

$\implies [2a - b - a + 2b][2a - b + a - 2b]$

Now, we can combine like terms and simplify:

$\implies [2a - b - a + 2b][2a - b + a - 2b]$

$\implies [a + b][3a - 3b]$

Three is common in 3a - 3b. Thus, we can factor 3 out of the expression:

$\implies [a + b][3a - 3b]$

$\implies [a + b] \times [3a - 3b]$

$\implies [a + b] \times 3[a - b]$

$\implies \boxed{3[a + b][a - b]}$

Therefore, 3[a + b][a - b] is the factorized expression of (2a - b)² - (a - 2b)²​.

Learn more about factoring expressions: brainly.com/question/1599970