Question

Simplify(x³-2x³+3x-4)(x-1)-(2x-3)(x²-x+1)​

Answer 1

Answer:

(x³-2x³+3x-4)(x-1)-(2x-3)(x²-x+1)​$= -x^4 - x^3+ 8x^2 - 12x +7$

Step-by-step explanation:

(x³-2x³+3x-4)(x-1)-(2x-3)(x²-x+1)​

First find the value of (x³-2x³+3x-4)(x-1)

= (x-1)  (x³-2x³+3x-4)

= (x-1)  ( - x³+3x-4)

= x ( - x³+3x-4)- 1 ( - x³+3x-4)

$= ( -x^4 + 3x^2 - 4x ) -(- x^3+3x-4)\\ = -x^4 + 3x^2 - 4x +x^3-3x+ 4\\ = -x^4+x^3 + 3x^2- 7x + 4$

then find the value of  (2x-3)(x²-x+1)​

(2x-3)(x²-x+1)​ = 2x(x²-x+1)​  - 3(x²-x+1)​

= 2x³ -2x² + 2x - 3x² +3x - 3

= 2x³ -5x² + 5x  - 3

So, (x³-2x³+3x-4)(x-1)-(2x-3)(x²-x+1)​

= $= (-x^4+x^3 + 3x^2- 7x + 4) -(2x^3 -5x^2+5x -3)\\= -x^4+x^3 + 3x^2- 7x + 4 - 2x^3 +5x^2-5x +3 \\= -x^4+x^3 - 2x^3+ 3x^2+5x^2- 7x -5x+ 4 +3\\= -x^4 - x^3+ 8x^2 - 12x +7$