What is factor (a^2-b^2)^2-(a-b)^4 ?

The solution to factor (a^2-b^2)^2-(a-b)^4 is 4ab(a-b)^2

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factor (a^2-b^2)^2-(a-b)^4

factor

(a^{2} - b^{2})^{2} - (a - b)^{4}

4 ab (a - b)^{2}

Solution steps

(a^{2} - b^{2})^{2} - (a - b)^{4}

Simplify

(a - b)^{4} : ((a - b)^{2})^{2}

= (a^{2} - b^{2})^{2} - ((a - b)^{2})^{2}

Apply Difference of Two Squares Formula:

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

(a^{2} - b^{2})^{2} - ((a - b)^{2})^{2} = ((a^{2} - b^{2}) + (a - b)^{2}) ((a^{2} - b^{2}) - (a - b)^{2})

= ((a^{2} - b^{2}) + (a - b)^{2}) ((a^{2} - b^{2}) - (a - b)^{2})

Factor

(a^{2} - b^{2}) + (a - b)^{2} : 2 a (a - b)

Factor

(a^{2} - b^{2}) - (a - b)^{2} : 2 b (a - b)

= 2 a (a - b) \cdot 2 b (a - b)

Simplify

2 a (a - b) \cdot 2 b (a - b) : 4 a (a - b)^{2} b

= 4 a (a - b)^{2} b

= 4 ab (a - b)^{2}

(a - 9) (2 a + 1) = 0

6 x^{2} - 8 = x

5 x - 8 \geq - 8 x + 18

x^{2} < 3 x

12 y^{2} + 21 y^{5}

What is factor (a^2-b^2)^2-(a-b)^4 ?
The solution to factor (a^2-b^2)^2-(a-b)^4 is 4ab(a-b)^2