What is expand (p+q)^6 ?

The solution to expand (p+q)^6 is p^6+6p^5q+15p^4q^2+20p^3q^3+15p^2q^4+6pq^5+q^6

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expand (p+q)^6

expand

(p + q)^{6}

p^{6} + 6 p^{5} q + 15 p^{4} q^{2} + 20 p^{3} q^{3} + 15 p^{2} q^{4} + 6 p q^{5} + q^{6}

Solution steps

(p + q)^{6}

Apply binomial theorem:

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

a = p, b = q

= i = 0 \sum 6 (i 6) p^{(6 - i)} q^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} p^{6} q^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} p^{5} q^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} p^{4} q^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} p^{3} q^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} p^{2} q^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} p^{1} q^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} p^{0} q^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} p^{6} q^{0} : p^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} p^{5} q^{1} : 6 p^{5} q

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} p^{4} q^{2} : 15 p^{4} q^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} p^{3} q^{3} : 20 p^{3} q^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} p^{2} q^{4} : 15 p^{2} q^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} p^{1} q^{5} : 6 p q^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} p^{0} q^{6} : q^{6}

= p^{6} + 6 p^{5} q + 15 p^{4} q^{2} + 20 p^{3} q^{3} + 15 p^{2} q^{4} + 6 p q^{5} + q^{6}

10. 1^{2}

- 24 - 12

8 x^{2} - 2 y^{2}

(8 h - 3) (3 h - 1)

- \frac{1}{2} (- \frac{1}{2})

What is expand (p+q)^6 ?
The solution to expand (p+q)^6 is p^6+6p^5q+15p^4q^2+20p^3q^3+15p^2q^4+6pq^5+q^6