Question

1) (a? – 5)(3 + 2a) – 2a(a? + 4); 2) (2 – 3a)3 – 4(2 - 9a) + 26a"; 3) (4 + a) – (a – 4)3 – 36(2a2 + 3). Вопрос это квадрат 60 балов

Answer 1

$\displaystyle \tt 1) \: (a^2-5)(3+2a)-2a(a^2+4)=3a^2+2a^3-15-10a-2a^3-8a=3a^2-18a-15\\\displaystyle \tt 2) \: (2-3a)^3-4(2-9a)+26a=8-36a+54a^2-27a^3-8+36a+26a=-27a^3+54a^2+26a\\\displaystyle \tt 3) \: (4+a)-(a-4)^3-36(2a^2+3)=4+a-(a^3-12a^2+48a-64)-72a^2-108=4+a-a^3+12a^2-48a+64-72a^2-108=-a^3-60a^2-47a-40$

Answer 2

To simplify the expressions and determine whether they are perfect squares, let's solve each of them step by step:

1. (a² – 5)(3 + 2a) – 2a(a² + 4)

Step 1: Distribute the first term: (a² – 5) * 3 + (a² – 5) * 2a

Step 2: Distribute the second term: 3a² - 15 + 2a³ - 10a

Step 3: Combine like terms: 2a³ + 3a² - 10a - 15

This expression is not a perfect square.

2. (2 – 3a)³ – 4(2 - 9a) + 26a

Step 1: Expand the cube using the formula (a - b)³ = a³ - 3a²b + 3ab² - b³: (2 - 3a)(2 - 3a)(2 - 3a)

Step 2: Expand each term: (4 - 12a + 9a²) - 4(2 - 9a) + 26a

Step 3: Simplify further: 4 - 12a + 9a² - 8 + 36a + 26a

Step 4: Combine like terms: 9a² + 62a - 4

This expression is not a perfect square.

3. (4 + a)² – (a – 4)³ – 36(2a² + 3)

Step 1: Expand the square using the formula (a + b)² = a² + 2ab + b²: (4 + a)(4 + a)

Step 2: Expand each term: 16 + 4a + 4a + a² - (a - 4)(a - 4)(a - 4)

Step 3: Expand the cube using the formula (a - b)³ = a³ - 3a²b + 3ab² - b³: a³ - 3a²(-4) + 3a(-4)² - (-4)³

Step 4: Simplify the cube: a³ + 12a² + 48a + 64

Step 5: Combine like terms: 16 + 8a + a² - (a³ + 12a² + 48a + 64) - 36(2a² + 3)

Step 6: Distribute -1 in the bracket and simplify further: 16 + 8a + a² - a³ - 12a² - 48a - 64 - 72a² - 108

Step 7: Combine like terms: -82a² + 8a + a² - a³ - 48

Step 8: Rearrange in descending order of powers: -a³ - 81a² + 8a - 48

This expression is not a perfect square.

None of the given expressions is a perfect square, so the answer to the question is that none of them is a square.