What is expand sqrt(4a^2(a-b)(a+b)+b^4) ?

The solution to expand sqrt(4a^2(a-b)(a+b)+b^4) is 2a^2-b^2

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expand sqrt(4a^2(a-b)(a+b)+b^4)

expand

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

2 a^{2} - b^{2}

Solution steps

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

Expand

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

= 4 a^{4} - 4 a^{2} b^{2} + b^{4}

Factor

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

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Apply radical rule:

assuming

a \geq 0

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

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

Apply radical rule:

assuming

a \geq 0

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

= (2 a + b) (2 a - b)

Apply Difference of Two Squares Formula:

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

a = 2 a, b = b

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

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

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

(x + y) (d + c + e)

\frac{x}{( 14.4 - x ) ^{4}}

\frac{5 x + 12}{x ( x - 7 ) ( x + 3 )}

5 (x + 9 = x - 3)

\frac{x ^{3}}{( x - 4 ) ( x + 3 )}

What is expand sqrt(4a^2(a-b)(a+b)+b^4) ?
The solution to expand sqrt(4a^2(a-b)(a+b)+b^4) is 2a^2-b^2