What is expand (3x^2-1)^5 ?

The solution to expand (3x^2-1)^5 is 243x^{10}-405x^8+270x^6-90x^4+15x^2-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x^2-1)^5

expand

(3 x^{2} - 1)^{5}

243 x^{10} - 405 x^{8} + 270 x^{6} - 90 x^{4} + 15 x^{2} - 1

Solution steps

(3 x^{2} - 1)^{5}

Apply binomial theorem:

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

a = 3 x^{2}, b = - 1

= i = 0 \sum 5 (i 5) (3 x^{2})^{(5 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x^{2})^{5} (- 1)^{0} : 243 x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x^{2})^{4} (- 1)^{1} : - 405 x^{8}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x^{2})^{3} (- 1)^{2} : 270 x^{6}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x^{2})^{2} (- 1)^{3} : - 90 x^{4}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x^{2})^{1} (- 1)^{4} : 15 x^{2}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x^{2})^{0} (- 1)^{5} : - 1

= 243 x^{10} - 405 x^{8} + 270 x^{6} - 90 x^{4} + 15 x^{2} - 1

sin^{2} (t) - cos^{2} (t)

(4 - 2 i) + (3 + 5 i)

\frac{1}{sin ( 2 x )}

\frac{4}{3} \cdot 3.14 \cdot 1 0^{3}

- 3 - i

What is expand (3x^2-1)^5 ?
The solution to expand (3x^2-1)^5 is 243x^{10}-405x^8+270x^6-90x^4+15x^2-1