Question

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

Answer 1

(x+1)(x²-2x+5)-(x²+3)(x-1) = x³ - 2x² + 5x + x² - 2x + 5 -(x³ - x² + 3x - 3 ) = x³ -x² +

+ 3x +5 - x³ + x² -3x + 3 = 8

Answer 2

Let's simplify the expression step by step:

1. Expand the first part: (x + 1)(x^2 - 2x + 5) = x(x^2 - 2x + 5) + 1(x^2 - 2x + 5) = x^3 - 2x^2 + 5x + x^2 - 2x + 5 = x^3 - x^2 + 3x + 5

2. Expand the second part: (x^2 + 3)(x - 1) = x^2(x - 1) + 3(x - 1) = x^3 - x^2 + 3x - 3

Now, subtract the expanded second part from the expanded first part:

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

Since the x^3 and x^2 terms have opposite signs in the parentheses, they will cancel out:

= x^3 - x^3 - x^2 + x^2 + 3x - 3x + 5 + 3 = 0 - 0 + 5 + 3 = 8

So, the simplified expression is 8.