What is factor 49x^4-4(x^2-3x)^2 ?

The solution to factor 49x^4-4(x^2-3x)^2 is 3x^2(3x-2)(5x+6)

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factor 49x^4-4(x^2-3x)^2

factor

49 x^{4} - 4 (x^{2} - 3 x)^{2}

3 x^{2} (3 x - 2) (5 x + 6)

Solution steps

49 x^{4} - 4 (x^{2} - 3 x)^{2}

49 x^{4} = (7 x^{2})^{2}

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

= (7 x^{2})^{2} - (2 (x^{2} - 3 x))^{2}

Apply Difference of Two Squares Formula:

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

(7 x^{2})^{2} - (2 (x^{2} - 3 x))^{2} = (7 x^{2} + 2 (x^{2} - 3 x)) (7 x^{2} - 2 (x^{2} - 3 x))

= (7 x^{2} + 2 (x^{2} - 3 x)) (7 x^{2} - 2 (x^{2} - 3 x))

Factor

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

Factor

7 x^{2} - 2 (x^{2} - 3 x) : x (5 x + 6)

= 3 x (3 x - 2) x (5 x + 6)

Apply exponent rule:

aa = a^{2}

xx = x^{2}

= 3 x^{2} (3 x - 2) (5 x + 6)

x - \frac{2 x - 1}{2} - \frac{2 x - 17}{16} = 1

2 x^{2} + 4 x - 2 = 0

\frac{12 x}{6 x y}

- 2 < 2 - 2 x \leq 12

s^{2} - 4 s = 0

What is factor 49x^4-4(x^2-3x)^2 ?
The solution to factor 49x^4-4(x^2-3x)^2 is 3x^2(3x-2)(5x+6)