Question

(3b-y)³(2a-5x)³(x²+5)³(2a³-3b²)³​

Answer 1

Ответ:

${(3b - y) }^{3} = 27 {b}^{3} - 27 {b}^{2} y + 9b {y}^{2} - {y}^{3} \\ (2a - 5x) ^{3} = 8 {a}^{3} - 60 {a}^{2} x + 150a {x}^{2} - 125a {x}^{3} \\ ( {x}^{2} + 5) ^{3} = {x}^{6} + 15 {x}^{5} + 75 {x}^{4} + 125 {x}^{3} \\ (2 {a}^{3} - 3 {b}^{2} ) ^{3} = 8 {a}^{9} - 36 {a}^{6} {b}^{2} + 54 {a}^{3} {b}^{4} - 27 {b}^{6}$

Answer 2

To simplify the expression (3b - y)³(2a - 5x)³(x² + 5)³(2a³ - 3b²)³, you can use the properties of exponents. First, let's simplify each term individually, and then multiply them together:

1. (3b - y)³: (3b - y)³ = (3b - y)(3b - y)(3b - y) Expand each term using the distributive property: (3b - y)(3b - y)(3b - y) = (9b² - 6by + y²)(3b - y) Now, multiply these two expressions: (9b² - 6by + y²)(3b - y) = 27b³ - 18b²y + 3by² - 9b²y + 6by² - y³

2. (2a - 5x)³: (2a - 5x)³ = (2a - 5x)(2a - 5x)(2a - 5x) Expand each term using the distributive property: (2a - 5x)(2a - 5x)(2a - 5x) = (4a² - 10ax + 25x²)(2a - 5x) Multiply these two expressions: (4a² - 10ax + 25x²)(2a - 5x) = 8a³ - 20a²x + 50ax² - 20a²x + 50x³ - 125x²

3. (x² + 5)³: (x² + 5)³ = (x² + 5)(x² + 5)(x² + 5) Expand each term using the distributive property: (x² + 5)(x² + 5)(x² + 5) = (x⁴ + 10x² + 25)(x² + 5) Multiply these two expressions: (x⁴ + 10x² + 25)(x² + 5) = x⁶ + 10x⁴ + 25x² + 5x² + 50x² + 125

4. (2a³ - 3b²)³: (2a³ - 3b²)³ = (2a³ - 3b²)(2a³ - 3b²)(2a³ - 3b²) Expand each term using the distributive property: (2a³ - 3b²)(2a³ - 3b²)(2a³ - 3b²) = (4a⁶ - 12a³b² + 9b⁴)(2a³ - 3b²) Multiply these two expressions: (4a⁶ - 12a³b² + 9b⁴)(2a³ - 3b²) = 8a⁹ - 24a⁶b² + 18a³b⁴ - 12a⁶b² + 36a³b⁴ - 27b⁶

Now, you can multiply all of these simplified expressions together:

(27b³ - 18b²y + 3by² - 9b²y + 6by² - y³)(8a³ - 20a²x + 50ax² - 20a²x + 50x³ - 125x²)(x⁶ + 10x⁴ + 25x² + 5x² + 50x² + 125)(8a⁹ - 24a⁶b² + 18a³b⁴ - 12a⁶b² + 36a³b⁴ - 27b⁶)

You can now simplify this massive expression by multiplying like terms and combining like terms, but it will be quite a lengthy and complex process. If you have specific values for 'a', 'b', 'x', and 'y', you can substitute them in and calculate the result numerically.