Question

Дам 80б. №1.(3x-5y^2)(3x+5y^2) №2.(a+2)(a^2-2a+4) №3.(x-1)(x^2+x+1) №4.какое равенство верно: а. (2a-3b^2)2=4a^2-6ab^2+9b^4 б. (x+3y)^2=x^2+9y^2+6xy №5.не решая пример,скажите,корректно (да) или некорректно (нет) следующие задания: 1) разделите многочлен 3x^2y-9xy^2 на одночлен 3x^2y 2) разделите многочлен 3xyz -9xy^2z на одночлен 3xy ответы: А.да,да Б.да,нет В.нет,да Г.нет,нет

Answer 1

Задание 4. Ответ б. Формула (а+б)^2+=а^2+2аб+б^2.

Answer 2

№1: To simplify the expression (3x-5y^2)(3x+5y^2), we can use the formula for the product of two binomials: (a + b)(a - b) = a^2 - b^2. Applying this formula, we have:

(3x-5y^2)(3x+5y^2) = (3x)^2 - (5y^2)^2 = 9x^2 - 25y^4

Therefore, the simplified expression for №1 is 9x^2 - 25y^4.

№2: To simplify the expression (a+2)(a^2-2a+4), we can use the distributive property of multiplication over addition. We multiply each term in the first binomial by each term in the second binomial and then combine like terms.

(a+2)(a^2-2a+4) = a(a^2-2a+4) + 2(a^2-2a+4) = a^3 - 2a^2 + 4a + 2a^2 - 4a + 8 = a^3 + 4

Therefore, the simplified expression for №2 is a^3 + 4.

№3: To simplify the expression (x-1)(x^2+x+1), we can again use the distributive property of multiplication over addition.

(x-1)(x^2+x+1) = x(x^2+x+1) - 1(x^2+x+1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1

Therefore, the simplified expression for №3 is x^3 - 1.

№4: Let's evaluate the expressions and determine which one is correct.

а. (2a-3b^2)^2 = (2a)^2 - 2(2a)(3b^2) + (3b^2)^2 = 4a^2 - 12ab^2 + 9b^4

б. (x+3y)^2 = (x)^2 + 2(x)(3y) + (3y)^2 = x^2 + 6xy + 9y^2

Therefore, the correct equality is а. (2a-3b^2)^2 = 4a^2 - 12ab^2 + 9b^4.

№5: Let's determine if the given division tasks are correct or not.

1) Divide the polynomial 3x^2y - 9xy^2 by the monomial 3x^2y.

To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial. In this case, each term of the polynomial is divisible by 3x^2y. Therefore, the division is correct.

2) Divide the polynomial 3xyz - 9xy^2z by the monomial 3xy.

Similarly, we divide each term of the polynomial by the monomial. In this case, the term 3xyz is divisible by 3xy, but the term -9xy^2z is not divisible. Therefore, the division is incorrect.

Therefore, the correct answer is Б. да, нет (Yes, No) for the given division tasks.