(x-1)(x^2-5x+7) (x-1)

2 min read Jun 17, 2024
(x-1)(x^2-5x+7) (x-1)

Expanding and Simplifying the Expression (x-1)(x^2-5x+7)(x-1)

This expression involves multiplying three factors together. Let's break down the steps to expand and simplify it:

Step 1: Multiply the first two factors

We start by multiplying the first two factors, (x-1) and (x^2-5x+7), using the distributive property (or FOIL method):

(x-1)(x^2-5x+7) = x(x^2-5x+7) - 1(x^2-5x+7) 

Expanding this further:

= x^3 - 5x^2 + 7x - x^2 + 5x - 7 

Combining like terms, we get:

= x^3 - 6x^2 + 12x - 7

Step 2: Multiply the result by the third factor

Now we need to multiply the result from Step 1, (x^3 - 6x^2 + 12x - 7), by the third factor, (x-1):

(x^3 - 6x^2 + 12x - 7)(x-1) = x(x^3 - 6x^2 + 12x - 7) - 1(x^3 - 6x^2 + 12x - 7)

Expanding:

= x^4 - 6x^3 + 12x^2 - 7x - x^3 + 6x^2 - 12x + 7

Finally, combining like terms:

= x^4 - 7x^3 + 18x^2 - 19x + 7 

Conclusion

Therefore, the simplified form of the expression (x-1)(x^2-5x+7)(x-1) is x^4 - 7x^3 + 18x^2 - 19x + 7.

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