What is expand ((b+x)^4)/4 ?

The solution to expand ((b+x)^4)/4 is (b^4)/4+b^3x+(3b^2x^2)/2+bx^3+(x^4)/4

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expand ((b+x)^4)/4

expand

\frac{( b + x ) ^{4}}{4}

\frac{b ^{4}}{4} + b^{3} x + \frac{3 b ^{2} x ^{2}}{2} + b x^{3} + \frac{x ^{4}}{4}

Solution steps

\frac{( b + x ) ^{4}}{4}

(b + x)^{4} = b^{4} + 4 b^{3} x + 6 b^{2} x^{2} + 4 b x^{3} + x^{4}

= \frac{b ^{4} + 4 b ^{3} x + 6 b ^{2} x ^{2} + 4 b x ^{3} + x ^{4}}{4}

Apply the fraction rule:

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

\frac{b ^{4} + 4 b ^{3} x + 6 b ^{2} x ^{2} + 4 b x ^{3} + x ^{4}}{4} = \frac{b ^{4}}{4} + \frac{4 b ^{3} x}{4} + \frac{6 b ^{2} x ^{2}}{4} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

= \frac{b ^{4}}{4} + \frac{4 b ^{3} x}{4} + \frac{6 b ^{2} x ^{2}}{4} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

Divide the numbers:

\frac{4}{4} = 1

= \frac{b ^{4}}{4} + b^{3} x + \frac{6 b ^{2} x ^{2}}{4} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

Cancel

\frac{6 b ^{2} x ^{2}}{4} : \frac{3 b ^{2} x ^{2}}{2}

= \frac{b ^{4}}{4} + b^{3} x + \frac{3 b ^{2} x ^{2}}{2} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

Divide the numbers:

\frac{4}{4} = 1

= \frac{b ^{4}}{4} + b^{3} x + \frac{3 b ^{2} x ^{2}}{2} + b x^{3} + \frac{x ^{4}}{4}

(x + 1)^{5} e^{3 x^{2}}

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\frac{d G - G ^{2} d H}{G ( 1 + G H )}

4^{\frac{3}{2}}

A (- 4, 2) B (6, 4) C (8, - 5)

What is expand ((b+x)^4)/4 ?
The solution to expand ((b+x)^4)/4 is (b^4)/4+b^3x+(3b^2x^2)/2+bx^3+(x^4)/4