Question

(2p-3)(2p+3)+(p-2)² объясните пожалуйста

Answer 1

To simplify the expression (2p-3)(2p+3)+(p-2)², we can use the distributive property and the formula for squaring a binomial.

Let's break it down step by step:

Step 1: Simplify the first part of the expression using the distributive property. (2p-3)(2p+3) can be expanded as follows: (2p)(2p) + (2p)(3) + (-3)(2p) + (-3)(3)

Simplifying further, we get: 4p² + 6p - 6p - 9

Combining like terms, we have: 4p² - 9

Step 2: Simplify the second part of the expression using the formula for squaring a binomial. (p-2)² can be expanded as follows: (p-2)(p-2)

Using the distributive property, we get: (p)(p) + (p)(-2) + (-2)(p) + (-2)(-2)

Simplifying further, we have: p² - 2p - 2p + 4

Combining like terms, we get: p² - 4p + 4

Step 3: Combine the simplified parts of the expression. Now, we can combine the simplified parts of the expression we obtained in Step 1 and Step 2: 4p² - 9 + p² - 4p + 4

Combining like terms, we have: 5p² - 4p - 5

So, the simplified expression is 5p² - 4p - 5.

I hope this explanation helps! Let me know if you have any further questions.