Question

21. 1) (2x - 3)2 – (3x – 5)"; 3) 16(2x + 5)2 - 81(4 - 5x)";5) (2a - 1)3 – 27aº;2) (3x + 2) - (1 - 2x)";4) 0,01a2 – (a - 3)2;6) (3x - 2) + (5 - 4x)".​

Answer 1

1)4х2-9-3х-5=4х2-3х-14

Answer 2

Let's simplify each of the given expressions:

1. (2x - 3)² - (3x - 5)

Expanding the squares: (2x - 3)(2x - 3) - (3x - 5)

Using the FOIL method: 4x² - 6x - 6x + 9 - (3x - 5)

Combining like terms: 4x² - 12x + 4

2. (3x + 2) - (1 - 2x)

Removing the parentheses: 3x + 2 - 1 + 2x

Combining like terms: 5x + 1

3. 16(2x + 5)² - 81(4 - 5x)

Expanding the squares: 16(4x² + 20x + 25) - 81(4 - 5x)

Distributing: 64x² + 320x + 400 - 324 + 405x

Combining like terms: 64x² + 725x + 76

4. 0.01a² - (a - 3)²

Expanding the square: 0.01a² - (a² - 2a + 1)

Distributing the negative sign: 0.01a² - a² + 2a - 1

Combining like terms: -0.99a² + 2a - 1

5. (2a - 1)³ - 27a⁰

Simplifying the exponent: (2a - 1)³ - 27

Using the formula for the cube of a binomial: (2a)³ - 3(2a)²(1) + 3(2a)(1)² - (1)³ - 27

Simplifying: 8a³ - 12a² + 6a - 1 - 27

Combining like terms: 8a³ - 12a² + 6a - 28

6. (3x - 2) + (5 - 4x)

Removing the parentheses: 3x - 2 + 5 - 4x

Combining like terms: -x + 3

So, the simplified expressions are:

1. 4x² - 12x + 4
2. 5x + 1
3. 64x² + 725x + 76
4. -0.99a² + 2a - 1
5. 8a³ - 12a² + 6a - 28
6. -x + 3