What is expand (2x-3)^7 ?

The solution to expand (2x-3)^7 is 128x^7-1344x^6+6048x^5-15120x^4+22680x^3-20412x^2+10206x-2187

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expand (2x-3)^7

expand

(2 x - 3)^{7}

128 x^{7} - 1344 x^{6} + 6048 x^{5} - 15120 x^{4} + 22680 x^{3} - 20412 x^{2} + 10206 x - 2187

Solution steps

(2 x - 3)^{7}

Apply binomial theorem:

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

a = 2 x, b = - 3

= i = 0 \sum 7 (i 7) (2 x)^{(7 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} (2 x)^{7} (- 3)^{0} : 128 x^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} (2 x)^{6} (- 3)^{1} : - 1344 x^{6}

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} (2 x)^{5} (- 3)^{2} : 6048 x^{5}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} (2 x)^{4} (- 3)^{3} : - 15120 x^{4}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} (2 x)^{3} (- 3)^{4} : 22680 x^{3}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} (2 x)^{2} (- 3)^{5} : - 20412 x^{2}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} (2 x)^{1} (- 3)^{6} : 10206 x

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} (2 x)^{0} (- 3)^{7} : - 2187

= 128 x^{7} - 1344 x^{6} + 6048 x^{5} - 15120 x^{4} + 22680 x^{3} - 20412 x^{2} + 10206 x - 2187

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

(\frac{100}{9})^{\frac{3}{2}}

2 - \frac{1}{4} (0.1)

0.125 \div 0.25 \times 6 - 0.24 \times 0.2

What is expand (2x-3)^7 ?
The solution to expand (2x-3)^7 is 128x^7-1344x^6+6048x^5-15120x^4+22680x^3-20412x^2+10206x-2187