What is ((x+y)^3-x^3)/y ?

The solution to ((x+y)^3-x^3)/y is 3x^2+3xy+y^2

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simplify ((x+y)^3-x^3)/y

simplify

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

3 x^{2} + 3 x y + y^{2}

Solution steps

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

Expand

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

= \frac{3 x ^{2} y + 3 x y ^{2} + y ^{3}}{y}

Factor

3 x^{2} y + 3 x y^{2} + y^{3} : y (3 x^{2} + 3 x y + y^{2})

= \frac{y ( 3 x ^{2} + 3 x y + y ^{2} )}{y}

Cancel the common factor:

y

= 3 x^{2} + 3 x y + y^{2}

100 + 8 - (- 8)

6 i - (14 - i) + (5 - 3 i)

∣ 1 - 3 ∣

5 k + 3 k^{3} + 7 k + 9 k^{3}

\frac{( 2 + i ) ( 3 + 2 i )}{( 1 - i ) i ^{3}}