What is expand (6-2x)^4 ?

The solution to expand (6-2x)^4 is 1296-1728x+864x^2-192x^3+16x^4

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expand (6-2x)^4

expand

(6 - 2 x)^{4}

1296 - 1728 x + 864 x^{2} - 192 x^{3} + 16 x^{4}

Solution steps

(6 - 2 x)^{4}

Apply binomial theorem:

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

a = 6, b = - 2 x

= i = 0 \sum 4 (i 4) \cdot 6^{(4 - i)} (- 2 x)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 6^{4} (- 2 x)^{0} : 1296

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 6^{3} (- 2 x)^{1} : - 1728 x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 6^{2} (- 2 x)^{2} : 864 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 6^{1} (- 2 x)^{3} : - 192 x^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 6^{0} (- 2 x)^{4} : 16 x^{4}

= 1296 - 1728 x + 864 x^{2} - 192 x^{3} + 16 x^{4}

\frac{( 8 ^{3} \cdot 36 - 2 ^{5} + 2 ^{3} + 16 + 2 )}{3}

(2 p + 2) (p - 2)

(- 1 + h)^{3}

(2 x + 4) (2 x + 4)

(3 x + 2 y) (9 x^{2} - 6 x y + 4 y^{2})

What is expand (6-2x)^4 ?
The solution to expand (6-2x)^4 is 1296-1728x+864x^2-192x^3+16x^4