Question

(5x^2-1)^2-3x^3(x^3-x+3)+3(x^2)-24

Answer 1

(5x² - 1)² - 3x³(x³ - x + 3) + 3(x²) - 24 = 25x⁴ - 10x² + 1 - 27(x³ - x) + 3x² - 24 = 25x⁴ - 10x² + 1 - 27x³ - 27x + 3x² - 24 = 25x⁴ - 7x² - 23 - 27x³ + 27x = 25x⁴ - 27x³ - 7x² + 27x - 23

Answer 2

To simplify the expression, let's start by expanding each term and then combine like terms:

(5x^2 - 1)^2 - 3x^3(x^3 - x + 3) + 3(x^2) - 24

Expanding the first term: (5x^2 - 1)(5x^2 - 1) = 25x^4 - 10x^2 + 1

Expanding the second term: -3x^3(x^3 - x + 3) = -3x^6 + 3x^4 - 9x^3

Combining like terms: (25x^4 - 10x^2 + 1) - (3x^6 - 3x^4 + 9x^3) + 3x^2 - 24

Now, let's simplify further by collecting like terms:

25x^4 - 10x^2 + 1 - 3x^6 + 3x^4 - 9x^3 + 3x^2 - 24

Grouping the terms: (-3x^6 + 25x^4 + 3x^4) + (-9x^3) + (3x^2 + 3x^2) + (-10x^2) + (1 - 24)

Simplifying: -3x^6 + 28x^4 - 9x^3 + 6x^2 - 23

So the simplified form of the expression (5x^2 - 1)^2 - 3x^3(x^3 - x + 3) + 3(x^2) - 24 is -3x^6 + 28x^4 - 9x^3 + 6x^2 - 23.