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

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

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expand (2x-y)^7

expand

(2 x - y)^{7}

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

Solution steps

(2 x - y)^{7}

Apply binomial theorem:

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

a = 2 x, b = - y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

10 \div 6 \frac{3}{7}

x^{2} - 36 z^{2}

\frac{( 6 \cdot 1 0 ^{8} )}{( 1.5 \cdot 1 0 ^{- 4} )}

- 7 \cdot (- 9)

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