Question

Помогите решить три примера по алгебре 7 класс. Задание упражнения "представьте выражение в виде квадрата двучлена,если это возможно" p²-2p+4= 49x²+12xy+64y²= 81y²-16z²-72yz= Всем заранее спасибо~

Answer 1

Невозможно по формуле о квадрате суммы(разности)

Answer 2

Solving Algebraic Expressions as Squares of Binomials

To solve the given algebraic expressions and represent them as squares of binomials, we will use the concept of perfect square trinomials. A perfect square trinomial is an expression that can be factored into the square of a binomial.

Let's solve each expression one by one:

1. p² - 2p + 4 = 49x² + 12xy + 64y²:

To represent the expression p² - 2p + 4 as a square of a binomial, we need to find two terms that, when squared, give us the given expression.

Let's complete the square for the left side of the equation:

p² - 2p + 4 = (p - 1)² + 3

Now, let's complete the square for the right side of the equation:

49x² + 12xy + 64y² = (7x + 4y)²

Therefore, the expression p² - 2p + 4 can be represented as the square of the binomial (p - 1)² + 3, and the expression 49x² + 12xy + 64y² can be represented as the square of the binomial (7x + 4y)².

2. 81y² - 16z² - 72yz:

To represent the expression 81y² - 16z² - 72yz as a square of a binomial, we need to find two terms that, when squared, give us the given expression.

Let's complete the square for the left side of the equation:

81y² - 16z² - 72yz = (9y - 4z)² - 144z²

Therefore, the expression 81y² - 16z² - 72yz can be represented as the square of the binomial (9y - 4z)² - 144z².

Please note that the given expressions may not always be possible to represent as squares of binomials. In such cases, we cannot find two terms that, when squared, give us the given expression.

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