Question

Представить трёхчлен 9х2 + 30х + 25 в виде квадрата двучлена. Представить трёхчлен а2 - 20аb2 +100 b4 в виде квадрата двучлена – квадрата разности. Представить трёхчлен 24аb -16а2 - 9 b2 в виде квадрата двучлена. ТОЛЬКО ПОЛНОЕ РЕШЕНИЕ!

Answer 1

Ответ:

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Answer 2

Representing a Three-Term Polynomial as the Square of a Binomial

To represent a three-term polynomial as the square of a binomial, we need to find two terms that, when squared, will give us the original polynomial. Let's go through each of the given three-term polynomials and find their representations.

1. Representing the polynomial 9x^2 + 30x + 25 as the square of a binomial:

To represent this polynomial as the square of a binomial, we need to find two terms that, when squared, will give us 9x^2 + 30x + 25. Let's start by looking at the first term, 9x^2. The square root of 9x^2 is 3x. Now, let's look at the last term, 25. The square root of 25 is 5. Therefore, we can represent the polynomial 9x^2 + 30x + 25 as the square of the binomial (3x + 5)^2.

2. Representing the polynomial a^2 - 20ab^2 + 100 + b^4 as the square of a binomial minus the square of a difference:

To represent this polynomial as the square of a binomial minus the square of a difference, we need to find two terms that, when squared and subtracted, will give us the original polynomial. Let's start by looking at the first term, a^2. The square root of a^2 is a. Now, let's look at the last term, b^4. The square root of b^4 is b^2. Therefore, we can represent the polynomial a^2 - 20ab^2 + 100 + b^4 as (a - b^2)^2 - (10b)^2.

3. Representing the polynomial 24ab - 16a^2 - 9 + b^2 as the square of a binomial:

To represent this polynomial as the square of a binomial, we need to find two terms that, when squared, will give us 24ab - 16a^2 - 9 + b^2. Let's start by looking at the first term, 24ab. The square root of 24ab is 2√6ab. Now, let's look at the last term, b^2. The square root of b^2 is b. Therefore, we can represent the polynomial 24ab - 16a^2 - 9 + b^2 as the square of the binomial (2√6ab + b)^2.

Please note that these representations are based on the given polynomials and may not be unique.