What is ((4a^4-8a^2*b^2+4b^4))/((a^2*b-b^3)) ?

The solution to ((4a^4-8a^2*b^2+4b^4))/((a^2*b-b^3)) is (4(a+b)(a-b))/b

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simplify ((4a^4-8a^2b^2+4b^4))/((a^2b-b^3))

simplify

\frac{( 4 a ^{4} - 8 a ^{2} \cdot b ^{2} + 4 b ^{4} )}{( a ^{2} \cdot b - b ^{3} )}

\frac{4 ( a + b ) ( a - b )}{b}

Solution steps

\frac{4 a ^{4} - 8 a ^{2} b ^{2} + 4 b ^{4}}{a ^{2} b - b ^{3}}

Factor

4 a^{4} - 8 a^{2} b^{2} + 4 b^{4} : 4 (a + b)^{2} (a - b)^{2}

= \frac{4 ( a + b ) ^{2} ( a - b ) ^{2}}{a ^{2} b - b ^{3}}

Factor

a^{2} b - b^{3} : b (a + b) (a - b)

= \frac{4 ( a + b ) ^{2} ( a - b ) ^{2}}{b ( a + b ) ( a - b )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= \frac{4 ( a + b ) ( a + b ) ( a - b ) ^{2}}{b ( a + b ) ( a - b )}

Cancel the common factor:

a + b

= \frac{4 ( a + b ) ( a - b ) ^{2}}{b ( a - b )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= \frac{4 ( a + b ) ( a - b ) ( a - b )}{b ( a - b )}

Cancel the common factor:

a - b

= \frac{4 ( a + b ) ( a - b )}{b}

(3 + 8) \cdot x^{6} - 42 - 7

\frac{1}{( x )}

x^{7} y^{7} - x y

2 x^{2} - 3 x y - 2 y^{2}

(x - y)^{10}

What is ((4a^4-8a^2*b^2+4b^4))/((a^2*b-b^3)) ?
The solution to ((4a^4-8a^2*b^2+4b^4))/((a^2*b-b^3)) is (4(a+b)(a-b))/b