What is expand (2+4y)^7 ?

The solution to expand (2+4y)^7 is 128+1792y+10752y^2+35840y^3+71680y^4+86016y^5+57344y^6+16384y^7

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expand (2+4y)^7

expand

(2 + 4 y)^{7}

128 + 1792 y + 10752 y^{2} + 35840 y^{3} + 71680 y^{4} + 86016 y^{5} + 57344 y^{6} + 16384 y^{7}

Solution steps

(2 + 4 y)^{7}

Apply binomial theorem:

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

a = 2, b = 4 y

= i = 0 \sum 7 (i 7) \cdot 2^{(7 - i)} (4 y)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 2^{7} (4 y)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 2^{6} (4 y)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 2^{5} (4 y)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 2^{4} (4 y)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 2^{3} (4 y)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 2^{2} (4 y)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 2^{1} (4 y)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 2^{0} (4 y)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 2^{7} (4 y)^{0} : 128

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 2^{6} (4 y)^{1} : 1792 y

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 2^{5} (4 y)^{2} : 10752 y^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 2^{4} (4 y)^{3} : 35840 y^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 2^{3} (4 y)^{4} : 71680 y^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 2^{2} (4 y)^{5} : 86016 y^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 2^{1} (4 y)^{6} : 57344 y^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 2^{0} (4 y)^{7} : 16384 y^{7}

= 128 + 1792 y + 10752 y^{2} + 35840 y^{3} + 71680 y^{4} + 86016 y^{5} + 57344 y^{6} + 16384 y^{7}

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What is expand (2+4y)^7 ?
The solution to expand (2+4y)^7 is 128+1792y+10752y^2+35840y^3+71680y^4+86016y^5+57344y^6+16384y^7