Question

1) (2а + 1)2 = 4а2 + 4а + 1 2) с2 – b2-7c+7b=(c-b)(c+b+7) 3) 729с3– 125b3 = (9с – 5b)(81с2+45cb+2 5b2) 4) (1,2у2 – 0,5х3)2 = 14,4у4- 1, 2х3у2 +0,25 х6 5) (m+3 )2 –(m-2)(m+2)= 6m+5 6) (3х + 2у)(2у – 3х) = 4у2 – 9х2 7) (5а + 3в)2 = 25а2 + 9в2 8) (4р – 5с)(4р + 5с) = 8р2 – 10с2

Answer 1

Ответ:

1)4а+2=4a²+4a+1

2-1=4a²+4a-4a

1=4a²

a²=0,25

a=0,5

Answer 2

It looks like you've provided several mathematical expressions and equations. Here's how each of them simplifies or factors:

1. $(2a + 1)^2 = 4a^2 + 4a + 1$

2. $c^2 - b^2 - 7c + 7b = (c - b)(c + b + 7)$

3. $729c^3 - 125b^3 = (9c - 5b)(81c^2 + 45cb + 25b^2)$

4. $(1.2y^2 - 0.5x^3)^2 = 14.4y^4 - 1.2x^3y^2 + 0.25x^6$

5. $(m + 3)^2 - (m - 2)(m + 2) = 6m + 5$

6. $(3x + 2y)(2y - 3x) = 4y^2 - 9x^2$

7. $(5a + 3b)^2 = 25a^2 + 9b^2$

8. $(4p - 5c)(4p + 5c) = 8p^2 - 10c^2$

These are the simplified forms or factorizations of the given expressions and equations. If you have any specific questions about any of these, please feel free to ask.

Answer 3

It seems like you have provided a set of algebraic expressions and equations. I'll go through each one and verify the given expressions or equations.

1. (2a + 1)² = 4a² + 4a + 1 This is correct. It represents the square of the binomial (2a + 1).

2. c² - b² - 7c + 7b = (c - b)(c + b + 7) This is also correct. It's the difference of squares factored into two binomials.

3. 729c³ - 125b³ = (9c - 5b)(81c² + 45cb + 25b²) This is correct. It's the difference of cubes factored using the difference of cubes formula.

4. (1.2y² - 0.5x³)² = 14.4y⁴ - 1.2x³y² + 0.25x⁶ This is correct, and it represents the square of the given expression.

5. (m + 3)² - (m - 2)(m + 2) = 6m + 5 This is also correct. It represents the expansion of the left side and simplifies to the right side.

6. (3x + 2y)(2y - 3x) = 4y² - 9x² This is correct. It represents the multiplication of two binomials and simplifies to the given expression.

7. (5a + 3b)² = 25a² + 9b² This is correct. It represents the square of the binomial (5a + 3b).

8. (4p - 5c)(4p + 5c) = 8p² - 10c² This is also correct. It represents the multiplication of two binomials and simplifies to the given expression.

All the provided expressions and equations are accurate and have been correctly identified or simplified.