What is expand ((ax+b)^3)/3 ?

The solution to expand ((ax+b)^3)/3 is (a^3x^3)/3+a^2bx^2+ab^2x+(b^3)/3

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expand ((ax+b)^3)/3

expand

\frac{( a x + b ) ^{3}}{3}

\frac{a ^{3} x ^{3}}{3} + a^{2} b x^{2} + a b^{2} x + \frac{b ^{3}}{3}

Solution steps

\frac{( a x + b ) ^{3}}{3}

(a x + b)^{3} = a^{3} x^{3} + 3 a^{2} b x^{2} + 3 a b^{2} x + b^{3}

= \frac{a ^{3} x ^{3} + 3 a ^{2} b x ^{2} + 3 a b ^{2} x + b ^{3}}{3}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{a ^{3} x ^{3} + 3 a ^{2} b x ^{2} + 3 a b ^{2} x + b ^{3}}{3} = \frac{a ^{3} x ^{3}}{3} + \frac{3 a ^{2} b x ^{2}}{3} + \frac{3 a b ^{2} x}{3} + \frac{b ^{3}}{3}

= \frac{a ^{3} x ^{3}}{3} + \frac{3 a ^{2} b x ^{2}}{3} + \frac{3 a b ^{2} x}{3} + \frac{b ^{3}}{3}

Divide the numbers:

\frac{3}{3} = 1

= \frac{a ^{3} x ^{3}}{3} + a^{2} b x^{2} + a b^{2} x + \frac{b ^{3}}{3}

\frac{( a + b ) ( c + 2 d + 3 )}{4}

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

\frac{( 1 + x )}{( 1 - x ) ^{2}}

D x [(x - 1) (4 - 2 x)]

(x + 1) \cdot e^{x}

What is expand ((ax+b)^3)/3 ?
The solution to expand ((ax+b)^3)/3 is (a^3x^3)/3+a^2bx^2+ab^2x+(b^3)/3