What is expand (m-2)(m^2-4)^2(m+2) ?

The solution to expand (m-2)(m^2-4)^2(m+2) is m^6-12m^4+48m^2-64

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (m-2)(m^2-4)^2(m+2)

expand

(m - 2) (m^{2} - 4)^{2} (m + 2)

m^{6} - 12 m^{4} + 48 m^{2} - 64

Solution steps

(m - 2) (m^{2} - 4)^{2} (m + 2)

= (m^{2} - 4)^{2} (m - 2) (m + 2)

Apply Difference of Two Squares

(m - 2) (m + 2) : m^{2} - 4

= (m^{2} - 4)^{2} (m^{2} - 4)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(m^{2} - 4)^{2} (m^{2} - 4) = (m^{2} - 4)^{2 + 1}

= (m^{2} - 4)^{2 + 1}

Add the numbers:

2 + 1 = 3

= (m^{2} - 4)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(m^{2} - 4)^{3} = (m^{2})^{3} - 3 (m^{2})^{2} \cdot 4 + 3 m^{2} \cdot 4^{2} - 4^{3}

= (m^{2})^{3} - 3 (m^{2})^{2} \cdot 4 + 3 m^{2} \cdot 4^{2} - 4^{3}

Simplify

(m^{2})^{3} - 3 (m^{2})^{2} \cdot 4 + 3 m^{2} \cdot 4^{2} - 4^{3} : m^{6} - 12 m^{4} + 48 m^{2} - 64

= m^{6} - 12 m^{4} + 48 m^{2} - 64

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

(- 7 + 7 i) - (3 + 2 i) - (i)

\frac{2}{8 - 7}

(2 x + 3) (2 x + 5)

\frac{x}{3} + \frac{x}{5}

What is expand (m-2)(m^2-4)^2(m+2) ?
The solution to expand (m-2)(m^2-4)^2(m+2) is m^6-12m^4+48m^2-64