What is expand (x^2-3)^7 ?

The solution to expand (x^2-3)^7 is x^{14}-21x^{12}+189x^{10}-945x^8+2835x^6-5103x^4+5103x^2-2187

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x^2-3)^7

expand

(x^{2} - 3)^{7}

x^{14} - 21 x^{12} + 189 x^{10} - 945 x^{8} + 2835 x^{6} - 5103 x^{4} + 5103 x^{2} - 2187

Solution steps

(x^{2} - 3)^{7}

Apply binomial theorem:

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

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

= i = 0 \sum 7 (i 7) (x^{2})^{(7 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} (x^{2})^{7} (- 3)^{0} : x^{14}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} (x^{2})^{6} (- 3)^{1} : - 21 x^{12}

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} (x^{2})^{5} (- 3)^{2} : 189 x^{10}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} (x^{2})^{4} (- 3)^{3} : - 945 x^{8}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} (x^{2})^{3} (- 3)^{4} : 2835 x^{6}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} (x^{2})^{2} (- 3)^{5} : - 5103 x^{4}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} (x^{2})^{1} (- 3)^{6} : 5103 x^{2}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} (x^{2})^{0} (- 3)^{7} : - 2187

= x^{14} - 21 x^{12} + 189 x^{10} - 945 x^{8} + 2835 x^{6} - 5103 x^{4} + 5103 x^{2} - 2187

\frac{( 2 b ) ^{3}}{6 b ^{5}}

(x + 2) (x + 3) - (x + 4) (x + 1)

(- 2) - (- 2)

[\frac{3 ( 2 a ) ^{3}}{2}]^{2}

What is expand (x^2-3)^7 ?
The solution to expand (x^2-3)^7 is x^{14}-21x^{12}+189x^{10}-945x^8+2835x^6-5103x^4+5103x^2-2187