What is expand (4-x)^7 ?

The solution to expand (4-x)^7 is 16384-28672x+21504x^2-8960x^3+2240x^4-336x^5+28x^6-x^7

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expand (4-x)^7

expand

(4 - x)^{7}

16384 - 28672 x + 21504 x^{2} - 8960 x^{3} + 2240 x^{4} - 336 x^{5} + 28 x^{6} - x^{7}

Solution steps

(4 - x)^{7}

Apply binomial theorem:

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

a = 4, b = - x

= i = 0 \sum 7 (i 7) \cdot 4^{(7 - i)} (- x)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 4^{7} (- x)^{0} : 16384

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 4^{6} (- x)^{1} : - 28672 x

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 4^{5} (- x)^{2} : 21504 x^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 4^{4} (- x)^{3} : - 8960 x^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 4^{3} (- x)^{4} : 2240 x^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 4^{2} (- x)^{5} : - 336 x^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 4^{1} (- x)^{6} : 28 x^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 4^{0} (- x)^{7} : - x^{7}

= 16384 - 28672 x + 21504 x^{2} - 8960 x^{3} + 2240 x^{4} - 336 x^{5} + 28 x^{6} - x^{7}

50 + 50 - 25 x^{0} + 1 - 2

(\frac{1}{5} a - \frac{1}{7} b - \frac{1}{3} c)^{2}

8 c^{2} + 5 c^{1} + 6 c^{2} + 7 c^{3} + 9 c^{4}

x^{2} (2 x + 3 y) + 3 x (2 x + 3 y) + 2 (2 x + 15 y)

- (0.1 k + 2)

What is expand (4-x)^7 ?
The solution to expand (4-x)^7 is 16384-28672x+21504x^2-8960x^3+2240x^4-336x^5+28x^6-x^7