Question

Which expression is equivalent to x^4 - 2x^3 + x^2?

x²(x - 1)²
x²(x + 1)2
ox? (x + 1)(x - 1)
6 x? (x² + 1) (x - 1)

Answer 1

x²(x - 1)²

Explanation

Given the expression x^4 - 2x^3 + x^2

Factoring out the common terms;

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

Factorize the expression in bracket

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

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

= x^2 (x(x-1)-1(x-1))

= x^2 (x-1)(x-1)

= x^2(x-1)^2

Hence the factored form of the expression is x²(x - 1)²