What is expand ((x^2+14x+48)(x+6))/2 ?

The solution to expand ((x^2+14x+48)(x+6))/2 is (x^3)/2+10x^2+66x+144

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expand ((x^2+14x+48)(x+6))/2

expand

\frac{( x ^{2} + 14 x + 48 ) ( x + 6 )}{2}

\frac{x ^{3}}{2} + 10 x^{2} + 66 x + 144

Solution steps

\frac{( x ^{2} + 14 x + 48 ) ( x + 6 )}{2}

Expand

(x^{2} + 14 x + 48) (x + 6) : x^{3} + 20 x^{2} + 132 x + 288

= \frac{x ^{3} + 20 x ^{2} + 132 x + 288}{2}

Apply the fraction rule:

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

\frac{x ^{3} + 20 x ^{2} + 132 x + 288}{2} = \frac{x ^{3}}{2} + \frac{20 x ^{2}}{2} + \frac{132 x}{2} + \frac{288}{2}

= \frac{x ^{3}}{2} + \frac{20 x ^{2}}{2} + \frac{132 x}{2} + \frac{288}{2}

Divide the numbers:

\frac{20}{2} = 10

= \frac{x ^{3}}{2} + 10 x^{2} + \frac{132 x}{2} + \frac{288}{2}

Divide the numbers:

\frac{132}{2} = 66

= \frac{x ^{3}}{2} + 10 x^{2} + 66 x + \frac{288}{2}

Divide the numbers:

\frac{288}{2} = 144

= \frac{x ^{3}}{2} + 10 x^{2} + 66 x + 144

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What is expand ((x^2+14x+48)(x+6))/2 ?
The solution to expand ((x^2+14x+48)(x+6))/2 is (x^3)/2+10x^2+66x+144