What is expand (a+b)^8 ?

The solution to expand (a+b)^8 is a^8+8a^7b+28a^6b^2+56a^5b^3+70a^4b^4+56a^3b^5+28a^2b^6+8ab^7+b^8

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expand (a+b)^8

expand

(a + b)^{8}

a^{8} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + b^{8}

Solution steps

(a + b)^{8}

Apply binomial theorem:

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

a = a, b = b

= i = 0 \sum 8 (i 8) a^{(8 - i)} b^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} a^{8} b^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} a^{7} b^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} a^{6} b^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} a^{5} b^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} a^{4} b^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} a^{3} b^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} a^{2} b^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} a^{1} b^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} a^{0} b^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} a^{8} b^{0} : a^{8}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} a^{7} b^{1} : 8 a^{7} b

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} a^{6} b^{2} : 28 a^{6} b^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} a^{5} b^{3} : 56 a^{5} b^{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} a^{4} b^{4} : 70 a^{4} b^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} a^{3} b^{5} : 56 a^{3} b^{5}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} a^{2} b^{6} : 28 a^{2} b^{6}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} a^{1} b^{7} : 8 a b^{7}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} a^{0} b^{8} : b^{8}

= a^{8} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + b^{8}

(x + 2) (x - 4)

lo g_{3} (15)

(x - 8) (x + 5)

(1 - 3 y)^{3}

(x + 3 y)^{2}

What is expand (a+b)^8 ?
The solution to expand (a+b)^8 is a^8+8a^7b+28a^6b^2+56a^5b^3+70a^4b^4+56a^3b^5+28a^2b^6+8ab^7+b^8