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Popular Algebra >

expand (3+2x)^8

Solution

expand

(3 + 2 x)^{8}

Solution

6561 + 34992 x + 81648 x^{2} + 108864 x^{3} + 90720 x^{4} + 48384 x^{5} + 16128 x^{6} + 3072 x^{7} + 256 x^{8}

Solution steps

(3 + 2 x)^{8}

Apply binomial theorem:

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

a = 3, b = 2 x

= i = 0 \sum 8 (i 8) \cdot 3^{(8 - i)} (2 x)^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 3^{8} (2 x)^{0} : 6561

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 3^{7} (2 x)^{1} : 34992 x

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 3^{6} (2 x)^{2} : 81648 x^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 3^{5} (2 x)^{3} : 108864 x^{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 3^{4} (2 x)^{4} : 90720 x^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 3^{3} (2 x)^{5} : 48384 x^{5}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 3^{2} (2 x)^{6} : 16128 x^{6}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 3^{1} (2 x)^{7} : 3072 x^{7}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 3^{0} (2 x)^{8} : 256 x^{8}

= 6561 + 34992 x + 81648 x^{2} + 108864 x^{3} + 90720 x^{4} + 48384 x^{5} + 16128 x^{6} + 3072 x^{7} + 256 x^{8}

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