What is expand ((a-b)^2x^3)/(102) ?

The solution to expand ((a-b)^2x^3)/(102) is (a^2x^3)/(102)-(abx^3)/(51)+(b^2x^3)/(102)

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expand ((a-b)^2x^3)/(102)

expand

\frac{( a - b ) ^{2} x ^{3}}{102}

\frac{a ^{2} x ^{3}}{102} - \frac{ab x ^{3}}{51} + \frac{b ^{2} x ^{3}}{102}

Solution steps

\frac{( a - b ) ^{2} x ^{3}}{102}

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

= \frac{x ^{3} ( a ^{2} - 2 ab + b ^{2} )}{102}

Expand

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

= \frac{a ^{2} x ^{3} - 2 ab x ^{3} + b ^{2} x ^{3}}{102}

Apply the fraction rule:

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

\frac{a ^{2} x ^{3} - 2 ab x ^{3} + b ^{2} x ^{3}}{102} = \frac{a ^{2} x ^{3}}{102} - \frac{2 ab x ^{3}}{102} + \frac{b ^{2} x ^{3}}{102}

= \frac{a ^{2} x ^{3}}{102} - \frac{2 ab x ^{3}}{102} + \frac{b ^{2} x ^{3}}{102}

Cancel

\frac{2 ab x ^{3}}{102} : \frac{ab x ^{3}}{51}

= \frac{a ^{2} x ^{3}}{102} - \frac{ab x ^{3}}{51} + \frac{b ^{2} x ^{3}}{102}

\frac{x - 5}{( x - 1 ) ^{3}}

f (x) = \frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}}

\frac{1}{5} (5 x ln (5 x - e) - 10 x - e ln (5 x - e) + 2 e = 44.8)

sin ((x + h)^{2})

(x - 7)^{6}

What is expand ((a-b)^2x^3)/(102) ?
The solution to expand ((a-b)^2x^3)/(102) is (a^2x^3)/(102)-(abx^3)/(51)+(b^2x^3)/(102)