What is factor 54(a+b)^3-27(a+b)^5 ?

The solution to factor 54(a+b)^3-27(a+b)^5 is -27(a+b)^3(a^2-2+2ab+b^2)

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factor 54(a+b)^3-27(a+b)^5

factor

54 (a + b)^{3} - 27 (a + b)^{5}

- 27 (a + b)^{3} (a^{2} - 2 + 2 ab + b^{2})

Solution steps

54 (a + b)^{3} - 27 (a + b)^{5}

Factor out common term

27 (a + b)^{3} : 27 (a + b)^{3} (2 - (a + b)^{2})

= 27 (a + b)^{3} (2 - (a + b)^{2})

Expand

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

= 27 (a + b)^{3} (2 - a^{2} - 2 ab - b^{2})

Factor

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

= 27 (a + b)^{3} (- (a^{2} - 2 + 2 ab + b^{2}))

Apply rule:

a (- b) = - ab

27 (a + b)^{3} (- (a^{2} - 2 + 2 ab + b^{2})) = - 27 (a + b)^{3} (a^{2} - 2 + 2 ab + b^{2})

= - 27 (a + b)^{3} (a^{2} - 2 + 2 ab + b^{2})

15 + 15

\frac{8 n ^{2} p ^{4}}{16 n ^{- 4} p ^{2}}

sin (\frac{x}{2}) cos (\frac{x}{2})

\frac{3 x}{x ^{2} - 81} - \frac{1}{x - 9}

(x^{2} - 2 x + 4)^{2}

What is factor 54(a+b)^3-27(a+b)^5 ?
The solution to factor 54(a+b)^3-27(a+b)^5 is -27(a+b)^3(a^2-2+2ab+b^2)