Answer:
x^4 -20x^3 +150x^2 -500x +625
Explanation:
You want the expansion of (x -5)^4 using the distributive property.
Squares
This can be written as ...
(x -5)^4 = ((x -5)^2)^2
Here's the expansion of the inner parentheses:
(x -5)^2 = (x -5)(x -5) = x(x -5) -5(x -5)
= x^2 -5x -5x +25 = x^2 -10x +25
Square again
Then the expansion of the outer parentheses is ...
(x^2 -10x +25)(x^2 -10x +25)
= x^2(x^2 -10x +25) -10x(x^2 -10x +25) +25(x^2 -10x +25)
= x^4 -10x^3 +25x^2 -10x^3 +100x^2 -250x +25x^2 -250x +625
(x -5)^4 = x^4 -20x^3 +150x^2 -500x +625
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Additional comment
If the 4 is intended to be a factor, then it distributes as ...
(x -5)(4) = (x)(4) -(5)(4) = 4x -20
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