What is expand (d-5y)^6 ?

The solution to expand (d-5y)^6 is d^6-30d^5y+375d^4y^2-2500d^3y^3+9375d^2y^4-18750dy^5+15625y^6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (d-5y)^6

expand

(d - 5 y)^{6}

d^{6} - 30 d^{5} y + 375 d^{4} y^{2} - 2500 d^{3} y^{3} + 9375 d^{2} y^{4} - 18750 d y^{5} + 15625 y^{6}

Solution steps

(d - 5 y)^{6}

Apply binomial theorem:

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

a = d, b = - 5 y

= i = 0 \sum 6 (i 6) d^{(6 - i)} (- 5 y)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} d^{6} (- 5 y)^{0} : d^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} d^{5} (- 5 y)^{1} : - 30 d^{5} y

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} d^{4} (- 5 y)^{2} : 375 d^{4} y^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} d^{3} (- 5 y)^{3} : - 2500 d^{3} y^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} d^{2} (- 5 y)^{4} : 9375 d^{2} y^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} d^{1} (- 5 y)^{5} : - 18750 d y^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} d^{0} (- 5 y)^{6} : 15625 y^{6}

= d^{6} - 30 d^{5} y + 375 d^{4} y^{2} - 2500 d^{3} y^{3} + 9375 d^{2} y^{4} - 18750 d y^{5} + 15625 y^{6}

\frac{3}{8} + \frac{4}{6}

x^{4} - x^{3} - 11 x^{2} + 5 x + 30

x^{3} + 3 x^{2} - 14 x - 20

- \frac{9}{2} + 7

x^{2} + (x + 2)^{2}

What is expand (d-5y)^6 ?
The solution to expand (d-5y)^6 is d^6-30d^5y+375d^4y^2-2500d^3y^3+9375d^2y^4-18750dy^5+15625y^6