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Popular >

expand (1+y)^5

Solution

expand

(1 + y)^{5}

Solution

1 + 5 y + 10 y^{2} + 10 y^{3} + 5 y^{4} + y^{5}

Solution steps

(1 + y)^{5}

Apply binomial theorem:

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

a = 1, b = y

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} y^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} y^{0} : 1

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} y^{1} : 5 y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} y^{2} : 10 y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} y^{3} : 10 y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} y^{4} : 5 y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} y^{5} : y^{5}

= 1 + 5 y + 10 y^{2} + 10 y^{3} + 5 y^{4} + y^{5}

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Frequently Asked Questions (FAQ)

What is expand (1+y)^5 ?
The solution to expand (1+y)^5 is 1+5y+10y^2+10y^3+5y^4+y^5