What is expand (x+a)^4 ?

The solution to expand (x+a)^4 is x^4+4ax^3+6a^2x^2+4a^3x+a^4

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expand (x+a)^4

expand

(x + a)^{4}

x^{4} + 4 a x^{3} + 6 a^{2} x^{2} + 4 a^{3} x + a^{4}

Solution steps

(x + a)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = a

= i = 0 \sum 4 (i 4) x^{(4 - i)} a^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} a^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} a^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} a^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} a^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} a^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} a^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} a^{1} : 4 a x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} a^{2} : 6 a^{2} x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} a^{3} : 4 a^{3} x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} a^{4} : a^{4}

= x^{4} + 4 a x^{3} + 6 a^{2} x^{2} + 4 a^{3} x + a^{4}

\frac{a + 2}{2 a + 4}

\frac{2 x ^{2} y}{x y - y}

936

\frac{1}{\frac{7}{2}}

- lo g_{10} (0.015)

What is expand (x+a)^4 ?
The solution to expand (x+a)^4 is x^4+4ax^3+6a^2x^2+4a^3x+a^4