Question

Спростити вираз (2х-1)²+(2х+1)² Прошу, дайте розгорнуту відповідь, буду дуже вдячна! Даю найвищий бал за гарну відповідь!

Answer 1

Согласно двум следующим формулам:
 $(a+b)^2=a^2+2ab+b^2\\ (a-b)^2=a^2-2ab+b^2$

имеем

$(2x-1)^2+(2x+1)^2=(2x)^2-2\cdot 1\cdot 2x+1^2+(2x)^2+2\cdot1\cdot 2x+1^2=\\ \\ \\ =4x^2-4x+1+4x^2+4x+1=8x^2+2=2(4x^2+1)$

Answer 2

Expanding the Expression (2x-1)² + (2x+1)²

To expand the given expression (2x-1)² + (2x+1)², we can use the formula for expanding the square of a binomial, which is (a+b)² = a² + 2ab + b². In this case, we have two binomials to expand, so we'll apply the formula to each binomial separately and then add the results together.

Expanding the first binomial (2x-1)²: 1. Square the first term: (2x)² = 4x² 2. Multiply the first and second terms by 2: 2 * 2x * (-1) = -4x 3. Square the second term: (-1)² = 1

So, the expanded form of (2x-1)² is 4x² - 4x + 1.

Expanding the second binomial (2x+1)²: 1. Square the first term: (2x)² = 4x² 2. Multiply the first and second terms by 2: 2 * 2x * 1 = 4x 3. Square the second term: (1)² = 1

So, the expanded form of (2x+1)² is 4x² + 4x + 1.

Now, adding the expanded forms of both binomials together: 4x² - 4x + 1 + 4x² + 4x + 1

Simplifying the expression: 8x² + 2

Therefore, the expanded form of (2x-1)² + (2x+1)² is 8x² + 2.

I hope this helps! If you have further questions or need additional assistance, feel free to ask!