Question

1) (x+y)² 2) (k-p)² 3) (2m+n)² 4) (3y-2x)² 5) (a-5s)² 6) (c+n)² 7) (5-m)² 8) (2b+2r)³ 9) (f+3)² 10) (7-y)² 11) (y²+1)² 12) (e²-6)² 13) (a²+3b)² 14) (p²-10)² 15) (5m²+2n²)² объясните как решать плиз

Answer 1

Если просто раскрыть скобки, то получиться это:

Answer 2

To simplify these expressions, we'll use the basic rules of algebra for expanding squared terms. The general formula for expanding the square of a binomial (a + b)² is (a + b)² = a² + 2ab + b².

Let's go through each expression one by one:

1. (x + y)² Expanding, we get: (x + y)² = x² + 2xy + y²

2. (k - p)² Expanding, we get: (k - p)² = k² - 2kp + p²

3. (2m + n)² Expanding, we get: (2m + n)² = (2m)² + 2 * 2m * n + n² = 4m² + 2mn + n²

4. (3y - 2x)² Expanding, we get: (3y - 2x)² = (3y)² - 2 * 3y * 2x + (2x)² = 9y² - 12xy + 4x²

5. (a - 5s)² Expanding, we get: (a - 5s)² = a² - 2 * a * 5s + (5s)² = a² - 10as + 25s²

6. (c + n)² Expanding, we get: (c + n)² = c² + 2cn + n²

7. (5 - m)² Expanding, we get: (5 - m)² = 5² - 2 * 5 * m + m² = 25 - 10m + m²

8. (2b + 2r)³ To expand the cube of a binomial (a + b)³, we use the formula (a + b)³ = a³ + 3a²b + 3ab² + b³. In this case, a = 2b and b = 2r. Expanding, we get: (2b + 2r)³ = (2b)³ + 3 * (2b)² * (2r) + 3 * 2b * (2r)² + (2r)³ = 8b³ + 24b²r + 24br² + 8r³

9. (f + 3)² Expanding, we get: (f + 3)² = f² + 2 * f * 3 + 3² = f² + 6f + 9

10. (7 - y)² Expanding, we get: (7 - y)² = 7² - 2 * 7 * y + y² = 49 - 14y + y²

11. (y² + 1)² Expanding, we get: (y² + 1)² = (y²)² + 2 * y² * 1 + 1² = y⁴ + 2y² + 1

12. (e² - 6)² Expanding, we get: (e² - 6)² = (e²)² - 2 * e² * 6 + 6² = e⁴ - 12e² + 36

13. (a² + 3b)² Expanding, we get: (a² + 3b)² = (a²)² + 2 * a² * 3b + (3b)² = a⁴ + 6a²b + 9b²

14. (p² - 10)² Expanding, we get: (p² - 10)² = (p²)² - 2 * p² * 10 + 10² = p⁴ - 20p² + 100

15. (5m² + 2n²)² Expanding, we get: (5m² + 2n²)² = (5m²)² + 2 * 5m² * 2n² + (2n²)² = 25m⁴ + 20m²n² + 4n⁴

These are the expanded forms of the given squared expressions. If you need further assistance or have any specific questions, feel free to ask!