Question

Раскрой скобки и определи степень многочлена 1) (2w³+7r²)(2w³-7r²) 2) (6х-9y⁶)(+9y⁶) 3) (9p⁴-12q⁴)(9p⁴+12q⁴)4) (x+y)(x-y)-x(x+2)+y²5) (3x-y)(3x+y)+y(y+4)-9x²6) (x-3y)(x+3y)-(x-y)²+10y²7) -(3x+y)²+(y-x)(x+y)+10x²Нужен только ответ помогите пожалуйста ​

Answer 1

1)4w^6-49r^4(степень многочлена 10)
2)54xy^6-81y^12(степень многочлена 18)
3)81p^8-144q^8(степень многочлена 16)
4)-2x

5)4y

6)2xy

7)-6xy

Answer 2

Expanding and Determining the Degree of Polynomials

To expand and determine the degree of each polynomial expression, let's go through each expression one by one:

1. (1 + (2w³ + 7r²))(2w³ - 7r²) - To expand this expression, we can use the distributive property. Multiply each term in the first set of parentheses by each term in the second set of parentheses. - The expanded form is: 2w³ + 7r² + 4w⁶ - 14w³r² - 7r⁴. - The degree of this polynomial is the highest exponent of the variable. In this case, the highest exponent is 6, so the degree is 6.

2. (6х - 9y⁶)(9y⁶) - To expand this expression, we can again use the distributive property. Multiply each term in the first set of parentheses by each term in the second set of parentheses. - The expanded form is: 54xy⁶ - 81y¹². - The degree of this polynomial is the highest exponent of the variable. In this case, the highest exponent is 12, so the degree is 12.

3. (9p⁴ - 12q⁴)(9p⁴ + 12q⁴) - Expanding this expression using the distributive property, we get: 81p⁸ - 144p⁴q⁴ + 144p⁴q⁴ - 144q⁸. - Simplifying further, we have: 81p⁸ - 144q⁸. - The degree of this polynomial is the highest exponent of the variable. In this case, the highest exponent is 8, so the degree is 8.

4. (x + y)(x - y) - x(x + 2) + y² - Expanding the first set of parentheses using the distributive property, we get: x² - xy + xy - y² - x² - 2x + y². - Simplifying further, we have: -2x. - The degree of this polynomial is the highest exponent of the variable. In this case, the highest exponent is 1, so the degree is 1.

5. (3x - y)(3x + y) + y(y + 4) - 9x² - Expanding the first set of parentheses using the distributive property, we get: 9x² - 3xy + 3xy - y² + y² + 4y - 9x². - Simplifying further, we have: 4y. - The degree of this polynomial is the highest exponent of the variable. In this case, the highest exponent is 1, so the degree is 1.

6. (x - 3y)(x + 3y) - (x - y)² + 10y² - Expanding the first set of parentheses using the distributive property, we get: x² - 3xy + 3xy - 9y² - (x - y)² + 10y². - Simplifying further, we have: x² - 9y² - (x - y)² + 10y². - The degree of this polynomial is the highest exponent of the variable. In this case, the highest exponent is 2, so the degree is 2.

7. -(3x + y)² + (y - x)(x + y) + 10x² - Expanding the first set of parentheses using the distributive property, we get: -(9x² + 6xy + y²) + (xy + y² - x² - xy) + 10x². - Simplifying further, we have: -9x² - 6xy - y² + xy + y² - x² + 10x². - Combining like terms, we get: x² - 5x² - 5xy. - Simplifying further, we have: -4x² - 5xy. - The degree of this polynomial is the highest exponent of the variable. In this case, the highest exponent is 2, so the degree is 2.

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