What is expand (h^4-81)/(h-3) ?

The solution to expand (h^4-81)/(h-3) is h^3+3h^2+9h+27

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expand (h^4-81)/(h-3)

expand

\frac{h ^{4} - 81}{h - 3}

h^{3} + 3 h^{2} + 9 h + 27

Solution steps

\frac{h ^{4} - 81}{h - 3}

Factor

h^{4} - 81 : (h^{2} + 9) (h + 3) (h - 3)

= \frac{( h ^{2} + 9 ) ( h + 3 ) ( h - 3 )}{h - 3}

Cancel the common factor:

h - 3

= (h^{2} + 9) (h + 3)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = h^{2}, b = 9, c = h, d = 3

= h^{2} h + h^{2} \cdot 3 + 9 h + 9 \cdot 3

= h^{2} h + 3 h^{2} + 9 h + 9 \cdot 3

Simplify

h^{2} h + 3 h^{2} + 9 h + 9 \cdot 3 : h^{3} + 3 h^{2} + 9 h + 27

= h^{3} + 3 h^{2} + 9 h + 27

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What is expand (h^4-81)/(h-3) ?
The solution to expand (h^4-81)/(h-3) is h^3+3h^2+9h+27