What is expand (3x-5y)^4 ?

The solution to expand (3x-5y)^4 is 81x^4-540x^3y+1350x^2y^2-1500xy^3+625y^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x-5y)^4

expand

(3 x - 5 y)^{4}

81 x^{4} - 540 x^{3} y + 1350 x^{2} y^{2} - 1500 x y^{3} + 625 y^{4}

Solution steps

(3 x - 5 y)^{4}

Apply binomial theorem:

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

a = 3 x, b = - 5 y

= i = 0 \sum 4 (i 4) (3 x)^{(4 - i)} (- 5 y)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x)^{4} (- 5 y)^{0} : 81 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (- 5 y)^{1} : - 540 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (- 5 y)^{2} : 1350 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} (- 5 y)^{3} : - 1500 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (- 5 y)^{4} : 625 y^{4}

= 81 x^{4} - 540 x^{3} y + 1350 x^{2} y^{2} - 1500 x y^{3} + 625 y^{4}

t^{2} - t - 6

6 - 8 i

(a^{3} b^{2} + 1)^{2}

(x^{\frac{1}{2}} + y^{\frac{1}{2}})^{12}

lo g_{10} (\frac{a}{b ^{2}})

What is expand (3x-5y)^4 ?
The solution to expand (3x-5y)^4 is 81x^4-540x^3y+1350x^2y^2-1500xy^3+625y^4