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

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

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

simplify

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

\frac{a - 2 b}{a ^{2} + 2 ab + 4 b ^{2}}

Solution steps

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

Factor

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

= \frac{( a - 2 b ) ^{2}}{a ^{3} - 8 b ^{3}}

Factor

a^{3} - 8 b^{3} : (a - 2 b) (a^{2} + 2 ab + 4 b^{2})

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

Apply exponent rule:

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

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

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

Cancel the common factor:

a - 2 b

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

15 \cdot (- 3)

- [5 (5 x^{2} + 3 x y - 7)] - x^{2}

35 \cdot 35 + 256 \cdot 999

\frac{2 ^{- 3} ( a w ) ^{- 1}}{a w ^{- 1} + 2 a y ^{- 1}}

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

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