Question

〖(2a-1)〗^2-(2a-3) (2a+3) упростить выражение

Answer 1

${(2a - 1)}^{2} - (2a - 3)(2a + 3) = 4 {a}^{2} - 4a + 1 - 4 {a}^{2} + 9 = 10 - 4a$

Answer 2

To simplify the expression 〖(2a-1)〗^2-(2a-3)(2a+3), we'll first expand the squared term and then multiply it with the second term before simplifying further. Let's proceed step by step:

Step 1: Expand the squared term (2a-1)² (2a-1)² = (2a-1)(2a-1) = 4a² - 2a - 2a + 1 = 4a² - 4a + 1

Step 2: Multiply the expanded squared term with the second term (2a-3)(2a+3) (2a-3)(2a+3) = 2a * 2a + 2a * 3 - 3 * 2a - 3 * 3 = 4a² + 6a - 6a - 9 = 4a² - 9

Now, the original expression becomes: 〖(2a-1)〗^2 - (2a-3)(2a+3) = (4a² - 4a + 1) - (4a² - 9)

Step 3: Combine like terms by removing parentheses and simplifying: = 4a² - 4a + 1 - 4a² + 9

Step 4: Combine the remaining like terms: = (4a² - 4a²) + (-4a + 9) + 1 = 0 - 4a + 9 + 1 = -4a + 10

So, the simplified expression is -4a + 10.