What is expand (qx+5)^5 ?

The solution to expand (qx+5)^5 is q^5x^5+25q^4x^4+250q^3x^3+1250q^2x^2+3125qx+3125

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expand (qx+5)^5

expand

(q x + 5)^{5}

q^{5} x^{5} + 25 q^{4} x^{4} + 250 q^{3} x^{3} + 1250 q^{2} x^{2} + 3125 q x + 3125

Solution steps

(q x + 5)^{5}

Apply binomial theorem:

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

a = q x, b = 5

= i = 0 \sum 5 (i 5) (q x)^{(5 - i)} \cdot 5^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (q x)^{5} \cdot 5^{0} : q^{5} x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (q x)^{4} \cdot 5^{1} : 25 q^{4} x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (q x)^{3} \cdot 5^{2} : 250 q^{3} x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (q x)^{2} \cdot 5^{3} : 1250 q^{2} x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (q x)^{1} \cdot 5^{4} : 3125 q x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (q x)^{0} \cdot 5^{5} : 3125

= q^{5} x^{5} + 25 q^{4} x^{4} + 250 q^{3} x^{3} + 1250 q^{2} x^{2} + 3125 q x + 3125

(2 x - 8) (2 x - 6)

6 \times 24

\frac{1}{3} \times 27

\frac{7}{7 - 2}

4 x^{4} - 24 x^{2} - 108

What is expand (qx+5)^5 ?
The solution to expand (qx+5)^5 is q^5x^5+25q^4x^4+250q^3x^3+1250q^2x^2+3125qx+3125