What is expand (2q-3)^4 ?

The solution to expand (2q-3)^4 is 16q^4-96q^3+216q^2-216q+81

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expand (2q-3)^4

expand

(2 q - 3)^{4}

16 q^{4} - 96 q^{3} + 216 q^{2} - 216 q + 81

Solution steps

(2 q - 3)^{4}

Apply binomial theorem:

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

a = 2 q, b = - 3

= i = 0 \sum 4 (i 4) (2 q)^{(4 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 q)^{4} (- 3)^{0} : 16 q^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 q)^{3} (- 3)^{1} : - 96 q^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 q)^{2} (- 3)^{2} : 216 q^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 q)^{1} (- 3)^{3} : - 216 q

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 q)^{0} (- 3)^{4} : 81

= 16 q^{4} - 96 q^{3} + 216 q^{2} - 216 q + 81

x (x)

lo g_{10} (- 3)

\frac{10}{24}

7 (- 5 v - 8)

(- \frac{15}{23}) + (- \frac{19}{23})

What is expand (2q-3)^4 ?
The solution to expand (2q-3)^4 is 16q^4-96q^3+216q^2-216q+81