Question

Simplify the following expressions

(x-2)(x+2)+(x+3)(x²-3x9)
-3x(x+2)²+(x+3)(x-1)(x+1)-(2x-3)²

Answer 1

To simplify the given expression, we expand each term and combine like terms.

Step-by-step explanation:

To simplify the given expression:

(x-2)(x+2) + (x+3)(x²-3x-9) - 3x(x+2)² + (x+3)(x-1)(x+1) - (2x-3)²

We can expand each term and then combine like terms:

1. (x-2)(x+2) = x² - 4
2. (x+3)(x²-3x-9) = x³ - 6x² - 30x - 27
3. 3x(x+2)² = 3x(x²+4x+4) = 3x³ + 12x² + 12x
4. (x+3)(x-1)(x+1) = (x²+2x-3)(x+1) = x⁴ + 2x³ - 3x² + x³ + 2x² - 3x - x² - 2x + 3
5. (2x-3)² = 4x² - 12x + 9

Combining all the terms, we have:

x² - 4 + x³ - 6x² - 30x - 27 - 3x³ - 12x² - 12x + x⁴ + 2x³ - 3x² + x³ + 2x² - 3x - x² - 2x + 3 - (4x² - 12x + 9)

Simplifying further, we get:

x⁴ - x³ - 4x² - 37x + 3