What is expand (a+2x)^7 ?

The solution to expand (a+2x)^7 is a^7+14a^6x+84a^5x^2+280a^4x^3+560a^3x^4+672a^2x^5+448ax^6+128x^7

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expand (a+2x)^7

expand

(a + 2 x)^{7}

a^{7} + 14 a^{6} x + 84 a^{5} x^{2} + 280 a^{4} x^{3} + 560 a^{3} x^{4} + 672 a^{2} x^{5} + 448 a x^{6} + 128 x^{7}

Solution steps

(a + 2 x)^{7}

Apply binomial theorem:

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

a = a, b = 2 x

= i = 0 \sum 7 (i 7) a^{(7 - i)} (2 x)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} a^{7} (2 x)^{0} : a^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} a^{6} (2 x)^{1} : 14 a^{6} x

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} a^{5} (2 x)^{2} : 84 a^{5} x^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} a^{4} (2 x)^{3} : 280 a^{4} x^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} a^{3} (2 x)^{4} : 560 a^{3} x^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} a^{2} (2 x)^{5} : 672 a^{2} x^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} a^{1} (2 x)^{6} : 448 a x^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} a^{0} (2 x)^{7} : 128 x^{7}

= a^{7} + 14 a^{6} x + 84 a^{5} x^{2} + 280 a^{4} x^{3} + 560 a^{3} x^{4} + 672 a^{2} x^{5} + 448 a x^{6} + 128 x^{7}

- 5 \times (- 6)

4 5^{2} + 9 0^{2}

\frac{9 - 10 i}{9 + i}

x^{4} - 13 x^{2} + 36

- 0.5 (0.7 q - 0.9) + 2 q

What is expand (a+2x)^7 ?
The solution to expand (a+2x)^7 is a^7+14a^6x+84a^5x^2+280a^4x^3+560a^3x^4+672a^2x^5+448ax^6+128x^7