Let's simplify the expression step by step:
Expand the expression:(x^2 - 5x + 6)^2 - 5(x^2 - 5x + 6) + 6= (x^2 - 5x + 6)(x^2 - 5x + 6) - 5x^2 + 25x - 30 + 6= (x^4 - 10x^3 + 36x^2 - 10x^3 + 100x^2 - 360x + 36x^2 - 360x + 1296) - 5x^2 + 25x - 24= x^4 - 10x^3 + 36x^2 - 10x^3 + 100x^2 - 360x + 36x^2 - 360x + 1296 - 5x^2 + 25x - 24
Combine like terms:= x^4 - 20x^3 + 172x^2 - 720x + 1296 - 5x^2 + 25x - 24
Simplify further:= x^4 - 20x^3 + 167x^2 - 695x + 1272
Therefore, the simplified expression is: x^4 - 20x^3 + 167x^2 - 695x + 1272
Let's simplify the expression step by step:
Expand the expression:
(x^2 - 5x + 6)^2 - 5(x^2 - 5x + 6) + 6
= (x^2 - 5x + 6)(x^2 - 5x + 6) - 5x^2 + 25x - 30 + 6
= (x^4 - 10x^3 + 36x^2 - 10x^3 + 100x^2 - 360x + 36x^2 - 360x + 1296) - 5x^2 + 25x - 24
= x^4 - 10x^3 + 36x^2 - 10x^3 + 100x^2 - 360x + 36x^2 - 360x + 1296 - 5x^2 + 25x - 24
Combine like terms:
= x^4 - 20x^3 + 172x^2 - 720x + 1296 - 5x^2 + 25x - 24
Simplify further:
= x^4 - 20x^3 + 167x^2 - 695x + 1272
Therefore, the simplified expression is: x^4 - 20x^3 + 167x^2 - 695x + 1272