What is factor (x^2-3x)^2-(x-3)^2 ?

The solution to factor (x^2-3x)^2-(x-3)^2 is (x-3)^2(x+1)(x-1)

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factor (x^2-3x)^2-(x-3)^2

factor

(x^{2} - 3 x)^{2} - (x - 3)^{2}

(x - 3)^{2} (x + 1) (x - 1)

Solution steps

(x^{2} - 3 x)^{2} - (x - 3)^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(x^{2} - 3 x)^{2} - (x - 3)^{2} = ((x^{2} - 3 x) + (x - 3)) ((x^{2} - 3 x) - (x - 3))

= ((x^{2} - 3 x) + (x - 3)) ((x^{2} - 3 x) - (x - 3))

Factor

(x^{2} - 3 x) + (x - 3) : (x - 3) (x + 1)

Factor

(x^{2} - 3 x) - (x - 3) : (x - 3) (x - 1)

= (x - 3) (x + 1) (x - 3) (x - 1)

Apply exponent rule:

aa = a^{2}

(x - 3) (x - 3) = (x - 3)^{2}

= (x - 3)^{2} (x + 1) (x - 1)

12 x - 8 = 1

x - 4 = 2^{3}

- 100 x^{5} + 90

- 6 x^{2} - 48 x - 72

(x + 6) (x - 6) = 13

What is factor (x^2-3x)^2-(x-3)^2 ?
The solution to factor (x^2-3x)^2-(x-3)^2 is (x-3)^2(x+1)(x-1)