What is expand (2x-1/2 y)^5 ?

The solution to expand (2x-1/2 y)^5 is (1024x^5-y^5}{32}-40x^4y+20x^3y^2-5x^2y^3+\frac{5xy^4)/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2x-1/2 y)^5

expand

(2 x - \frac{1}{2} y)^{5}

\frac{1024 x ^{5} - y ^{5}}{32} - 40 x^{4} y + 20 x^{3} y^{2} - 5 x^{2} y^{3} + \frac{5 x y ^{4}}{8}

Solution steps

(2 x - \frac{1}{2} y)^{5}

Apply binomial theorem:

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

a = 2 x, b = - \frac{1}{2} y

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} (- \frac{1}{2} y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} (- \frac{1}{2} y)^{0} : 32 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x)^{4} (- \frac{1}{2} y)^{1} : - 40 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} (- \frac{1}{2} y)^{2} : 20 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} (- \frac{1}{2} y)^{3} : - 5 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x)^{1} (- \frac{1}{2} y)^{4} : \frac{5 x y ^{4}}{8}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} (- \frac{1}{2} y)^{5} : - \frac{y ^{5}}{32}

= 32 x^{5} - 40 x^{4} y + 20 x^{3} y^{2} - 5 x^{2} y^{3} + \frac{5 x y ^{4}}{8} - \frac{y ^{5}}{32}

Join

32 x^{5} - 40 x^{4} y + 20 x^{3} y^{2} - 5 x^{2} y^{3} + \frac{5 x y ^{4}}{8} - \frac{y ^{5}}{32} : \frac{1024 x ^{5} - y ^{5}}{32} - 40 x^{4} y + 20 x^{3} y^{2} - 5 x^{2} y^{3} + \frac{5 x y ^{4}}{8}

= \frac{1024 x ^{5} - y ^{5}}{32} - 40 x^{4} y + 20 x^{3} y^{2} - 5 x^{2} y^{3} + \frac{5 x y ^{4}}{8}

\frac{16 s}{( s ^{2} + 1 ) ^{2} ( s ^{2} + 4 )}

\frac{v + 6}{( v + 8 ) ( v - 4 )}

\frac{5}{2 ( 1 + 2 i ) ^{2}}

5 - (\frac{5 ( 3 - 3 )}{3})

T 2^{2} (T^{2} - 1.9044 = 2405.6014)

What is expand (2x-1/2 y)^5 ?
The solution to expand (2x-1/2 y)^5 is (1024x^5-y^5}{32}-40x^4y+20x^3y^2-5x^2y^3+\frac{5xy^4)/8