What is expand (1-2x)^7 ?

The solution to expand (1-2x)^7 is 1-14x+84x^2-280x^3+560x^4-672x^5+448x^6-128x^7

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expand (1-2x)^7

expand

(1 - 2 x)^{7}

1 - 14 x + 84 x^{2} - 280 x^{3} + 560 x^{4} - 672 x^{5} + 448 x^{6} - 128 x^{7}

Solution steps

(1 - 2 x)^{7}

Apply binomial theorem:

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

a = 1, b = - 2 x

= i = 0 \sum 7 (i 7) \cdot 1^{(7 - i)} (- 2 x)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 1^{7} (- 2 x)^{0} : 1

Simplify

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

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 1^{5} (- 2 x)^{2} : 84 x^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 1^{4} (- 2 x)^{3} : - 280 x^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 1^{3} (- 2 x)^{4} : 560 x^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 1^{2} (- 2 x)^{5} : - 672 x^{5}

Simplify

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

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 1^{0} (- 2 x)^{7} : - 128 x^{7}

= 1 - 14 x + 84 x^{2} - 280 x^{3} + 560 x^{4} - 672 x^{5} + 448 x^{6} - 128 x^{7}

\frac{3 x y ^{2}}{9 x ^{8} y ^{6}}

\frac{15 2}{2}

(- 2)^{2} + (2)^{2}

\frac{( - 8 x ^{- 3} y ) ^{2} ( - 2 z ) ^{3} ( - 2 z ) ^{3}}{512 x ^{- 7} y ^{2}}

\frac{38}{100}

What is expand (1-2x)^7 ?
The solution to expand (1-2x)^7 is 1-14x+84x^2-280x^3+560x^4-672x^5+448x^6-128x^7