Question

Преобразуйте в многочлен стандартного вида:а)(2x-3y)(2x+3y);б)(а-5)в квадрате-2а(а-3).

Answer 1

а)2х²+3у²

б)а²-10а+25-2а²+6=-а²-10а+31

Answer 2

a) 4^2 - 9y^2 

b) a^2 - 10a +25 - 2a^2 + 6a =  -a^2 - 4a +25 

Answer 3

а) (2x-3y)(2x+3y)

To expand the expression (2x-3y)(2x+3y) into standard form, we can use the distributive property.

The distributive property states that for any real numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b and a and c.

Applying the distributive property to the given expression, we get:

(2x-3y)(2x+3y) = 2x * 2x + 2x * 3y - 3y * 2x - 3y * 3y

Simplifying further, we have:

= 4x^2 + 6xy - 6xy - 9y^2

The middle terms, 2x * 3y and -3y * 2x, cancel each other out because they have opposite signs and the same value.

Therefore, the expanded form of (2x-3y)(2x+3y) is:

4x^2 - 9y^2.

б) (а-5)в квадрате - 2а(а-3)

To expand the expression (а-5)в квадрате - 2а(а-3) into standard form, we can use the distributive property and the formula for squaring a binomial.

First, let's square the binomial (а-5):

(а-5)в квадрате = (а-5)(а-5)

Using the distributive property, we get:

= а * а - 5 * а - 5 * а + 5 * 5

Simplifying further, we have:

= а^2 - 10а + 25

Next, let's simplify the expression - 2а(а-3):

- 2а(а-3) = -2а * а + (-2а) * (-3)

Using the distributive property, we get:

= -2а^2 + 6а

Now, let's substitute the simplified expressions back into the original expression:

(а-5)в квадрате - 2а(а-3) = (а^2 - 10а + 25) - 2а^2 + 6а

Expanding further, we have:

= а^2 - 10а + 25 - 2а^2 + 6а

Combining like terms, we get:

= -а^2 - 4а + 25

Therefore, the expanded form of (а-5)в квадрате - 2а(а-3) is:

-а^2 - 4а + 25.