What is expand (1+2/3 x)^8(3+8x)^2 ?

The solution to expand (1+2/3 x)^8(3+8x)^2 is

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expand (1+2/3 x)^8(3+8x)^2

expand

(1 + \frac{2}{3} x)^{8} (3 + 8 x)^{2}

9 + 96 x + 432 x^{2} + 1088 x^{3} + \frac{5152 x ^{4}}{3} + 1792 x^{5} + \frac{34048 x ^{6}}{27} + \frac{48128 x ^{7}}{81} + \frac{4864 x ^{8}}{27} + \frac{69632 x ^{9}}{2187} + \frac{16384 x ^{10}}{6561}

Solution steps

(1 + \frac{2}{3} x)^{8} (3 + 8 x)^{2}

Expand

(3 + 8 x)^{2} : 9 + 48 x + 64 x^{2}

= (1 + \frac{2}{3} x)^{8} (9 + 48 x + 64 x^{2})

Apply the distributive law:

m (a + b + c) = ma + mb + m c

(1 + \frac{2}{3} x)^{8} (9 + 48 x + 64 x^{2}) = (1 + \frac{2}{3} x)^{8} \cdot 9 + (1 + \frac{2}{3} x)^{8} \cdot 48 x + (1 + \frac{2}{3} x)^{8} \cdot 64 x^{2}

= (1 + \frac{2}{3} x)^{8} \cdot 9 + (1 + \frac{2}{3} x)^{8} \cdot 48 x + (1 + \frac{2}{3} x)^{8} \cdot 64 x^{2}

= 9 (1 + \frac{2}{3} x)^{8} + 48 x (1 + \frac{2}{3} x)^{8} + 64 x^{2} (1 + \frac{2}{3} x)^{8}

Expand

9 (1 + \frac{2}{3} x)^{8} : 9 + 48 x + 112 x^{2} + \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{9} + \frac{1792 x ^{5}}{27} + \frac{1792 x ^{6}}{81} + \frac{1024 x ^{7}}{243} + \frac{256 x ^{8}}{729}

= 9 + 48 x + 112 x^{2} + \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{9} + \frac{1792 x ^{5}}{27} + \frac{1792 x ^{6}}{81} + \frac{1024 x ^{7}}{243} + \frac{256 x ^{8}}{729} + 48 x (1 + \frac{2}{3} x)^{8} + 64 x^{2} (1 + \frac{2}{3} x)^{8}

Expand

48 x (1 + \frac{2}{3} x)^{8} : 48 x + 256 x^{2} + \frac{1792 x ^{3}}{3} + \frac{7168 x ^{4}}{9} + \frac{17920 x ^{5}}{27} + \frac{28672 x ^{6}}{81} + \frac{28672 x ^{7}}{243} + \frac{16384 x ^{8}}{729} + \frac{4096 x ^{9}}{2187}

= 9 + 48 x + 112 x^{2} + \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{9} + \frac{1792 x ^{5}}{27} + \frac{1792 x ^{6}}{81} + \frac{1024 x ^{7}}{243} + \frac{256 x ^{8}}{729} + 48 x + 256 x^{2} + \frac{1792 x ^{3}}{3} + \frac{7168 x ^{4}}{9} + \frac{17920 x ^{5}}{27} + \frac{28672 x ^{6}}{81} + \frac{28672 x ^{7}}{243} + \frac{16384 x ^{8}}{729} + \frac{4096 x ^{9}}{2187} + 64 x^{2} (1 + \frac{2}{3} x)^{8}

Expand

64 x^{2} (1 + \frac{2}{3} x)^{8} : 64 x^{2} + \frac{1024 x ^{3}}{3} + \frac{7168 x ^{4}}{9} + \frac{28672 x ^{5}}{27} + \frac{71680 x ^{6}}{81} + \frac{114688 x ^{7}}{243} + \frac{114688 x ^{8}}{729} + \frac{65536 x ^{9}}{2187} + \frac{16384 x ^{10}}{6561}

= 9 + 48 x + 112 x^{2} + \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{9} + \frac{1792 x ^{5}}{27} + \frac{1792 x ^{6}}{81} + \frac{1024 x ^{7}}{243} + \frac{256 x ^{8}}{729} + 48 x + 256 x^{2} + \frac{1792 x ^{3}}{3} + \frac{7168 x ^{4}}{9} + \frac{17920 x ^{5}}{27} + \frac{28672 x ^{6}}{81} + \frac{28672 x ^{7}}{243} + \frac{16384 x ^{8}}{729} + \frac{4096 x ^{9}}{2187} + 64 x^{2} + \frac{1024 x ^{3}}{3} + \frac{7168 x ^{4}}{9} + \frac{28672 x ^{5}}{27} + \frac{71680 x ^{6}}{81} + \frac{114688 x ^{7}}{243} + \frac{114688 x ^{8}}{729} + \frac{65536 x ^{9}}{2187} + \frac{16384 x ^{10}}{6561}

Simplify

9 + 48 x + 112 x^{2} + \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{9} + \frac{1792 x ^{5}}{27} + \frac{1792 x ^{6}}{81} + \frac{1024 x ^{7}}{243} + \frac{256 x ^{8}}{729} + 48 x + 256 x^{2} + \frac{1792 x ^{3}}{3} + \frac{7168 x ^{4}}{9} + \frac{17920 x ^{5}}{27} + \frac{28672 x ^{6}}{81} + \frac{28672 x ^{7}}{243} + \frac{16384 x ^{8}}{729} + \frac{4096 x ^{9}}{2187} + 64 x^{2} + \frac{1024 x ^{3}}{3} + \frac{7168 x ^{4}}{9} + \frac{28672 x ^{5}}{27} + \frac{71680 x ^{6}}{81} + \frac{114688 x ^{7}}{243} + \frac{114688 x ^{8}}{729} + \frac{65536 x ^{9}}{2187} + \frac{16384 x ^{10}}{6561} : 9 + 96 x + 432 x^{2} + 1088 x^{3} + \frac{5152 x ^{4}}{3} + 1792 x^{5} + \frac{34048 x ^{6}}{27} + \frac{48128 x ^{7}}{81} + \frac{4864 x ^{8}}{27} + \frac{69632 x ^{9}}{2187} + \frac{16384 x ^{10}}{6561}

= 9 + 96 x + 432 x^{2} + 1088 x^{3} + \frac{5152 x ^{4}}{3} + 1792 x^{5} + \frac{34048 x ^{6}}{27} + \frac{48128 x ^{7}}{81} + \frac{4864 x ^{8}}{27} + \frac{69632 x ^{9}}{2187} + \frac{16384 x ^{10}}{6561}

\frac{( x - 1 ) ( x - 3 )}{( x - 2 ) ^{2}}

(cos (2 π t) - 2 π t sin (2 π t))^{2}

C (2, - 5)

(6 - i)^{6}

\frac{( x - 1 ) ^{2}}{3}

What is expand (1+2/3 x)^8(3+8x)^2 ?
The solution to expand (1+2/3 x)^8(3+8x)^2 is