What is expand (5x^2-2)^4 ?

The solution to expand (5x^2-2)^4 is 625x^8-1000x^6+600x^4-160x^2+16

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (5x^2-2)^4

expand

(5 x^{2} - 2)^{4}

625 x^{8} - 1000 x^{6} + 600 x^{4} - 160 x^{2} + 16

Solution steps

(5 x^{2} - 2)^{4}

Apply binomial theorem:

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

a = 5 x^{2}, b = - 2

= i = 0 \sum 4 (i 4) (5 x^{2})^{(4 - i)} (- 2)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 x^{2})^{4} (- 2)^{0} : 625 x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x^{2})^{3} (- 2)^{1} : - 1000 x^{6}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x^{2})^{2} (- 2)^{2} : 600 x^{4}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x^{2})^{1} (- 2)^{3} : - 160 x^{2}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 x^{2})^{0} (- 2)^{4} : 16

= 625 x^{8} - 1000 x^{6} + 600 x^{4} - 160 x^{2} + 16

\frac{3}{5} + \frac{7}{10}

2 x^{2} + x + 4 x + 2

\frac{m - p}{n} - \frac{n + x}{m}

\frac{x}{y} \cdot \frac{z}{w}

(2 y^{5})^{3}

What is expand (5x^2-2)^4 ?
The solution to expand (5x^2-2)^4 is 625x^8-1000x^6+600x^4-160x^2+16