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Popular >

expand (y+2)^4

Solution

expand

(y + 2)^{4}

Solution

y^{4} + 8 y^{3} + 24 y^{2} + 32 y + 16

Solution steps

(y + 2)^{4}

Apply binomial theorem:

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

a = y, b = 2

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} y^{4} \cdot 2^{0} : y^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} y^{3} \cdot 2^{1} : 8 y^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} y^{2} \cdot 2^{2} : 24 y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} y^{1} \cdot 2^{3} : 32 y

Simplify

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

= y^{4} + 8 y^{3} + 24 y^{2} + 32 y + 16

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Frequently Asked Questions (FAQ)

What is expand (y+2)^4 ?
The solution to expand (y+2)^4 is y^4+8y^3+24y^2+32y+16