Question

(x-2)(x²+2x+4)-(1+x)(x²-x+1)= Упростить выражение

Answer 1

...=x^3+2x^2+4x-2x^2-2x-8-x^2-x-1+x^3-x^2+x=2x^3-2x^2+2x-9=x^3-x^2+x-4,5

Answer 2

To simplify the given expression, let's start by expanding and then combining like terms:

Given expression: (x-2)(x²+2x+4) - (1+x)(x²-x+1)

Step 1: Expand both terms (x-2)(x²+2x+4) = x(x²+2x+4) - 2(x²+2x+4) = x³ + 2x² + 4x - 2x² - 4x - 8

(1+x)(x²-x+1) = 1(x²-x+1) + x(x²-x+1) = x² - x + 1 + x³ - x² + x = x³ - x² + x - x + 1

Step 2: Combine like terms x³ + 2x² + 4x - 2x² - 4x - 8 - (x³ - x² + x - x + 1)

Step 3: Remove parentheses and combine terms x³ + 2x² + 4x - 2x² - 4x - 8 - x³ + x² - x + x - 1

Step 4: Simplify further (x³ - x³) + (2x² - 2x²) + (4x - 4x) + (-x + x) - 8 - 1

Step 5: The terms with the same variables cancel each other out 0x³ + 0x² + 0x - 9

Step 6: Simplified expression -9

So, the simplified form of the given expression is -9.