What is expand (y+z)^7-(y-z)^7 ?

The solution to expand (y+z)^7-(y-z)^7 is 14y^6z+70y^4z^3+42y^2z^5+2z^7

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expand (y+z)^7-(y-z)^7

expand

(y + z)^{7} - (y - z)^{7}

14 y^{6} z + 70 y^{4} z^{3} + 42 y^{2} z^{5} + 2 z^{7}

Solution steps

(y + z)^{7} - (y - z)^{7}

Expand

(y + z)^{7} : y^{7} + 7 y^{6} z + 21 y^{5} z^{2} + 35 y^{4} z^{3} + 35 y^{3} z^{4} + 21 y^{2} z^{5} + 7 y z^{6} + z^{7}

= y^{7} + 7 y^{6} z + 21 y^{5} z^{2} + 35 y^{4} z^{3} + 35 y^{3} z^{4} + 21 y^{2} z^{5} + 7 y z^{6} + z^{7} - (y - z)^{7}

Expand

- (y - z)^{7} : - y^{7} + 7 y^{6} z - 21 y^{5} z^{2} + 35 y^{4} z^{3} - 35 y^{3} z^{4} + 21 y^{2} z^{5} - 7 y z^{6} + z^{7}

= y^{7} + 7 y^{6} z + 21 y^{5} z^{2} + 35 y^{4} z^{3} + 35 y^{3} z^{4} + 21 y^{2} z^{5} + 7 y z^{6} + z^{7} - y^{7} + 7 y^{6} z - 21 y^{5} z^{2} + 35 y^{4} z^{3} - 35 y^{3} z^{4} + 21 y^{2} z^{5} - 7 y z^{6} + z^{7}

Simplify

y^{7} + 7 y^{6} z + 21 y^{5} z^{2} + 35 y^{4} z^{3} + 35 y^{3} z^{4} + 21 y^{2} z^{5} + 7 y z^{6} + z^{7} - y^{7} + 7 y^{6} z - 21 y^{5} z^{2} + 35 y^{4} z^{3} - 35 y^{3} z^{4} + 21 y^{2} z^{5} - 7 y z^{6} + z^{7} : 14 y^{6} z + 70 y^{4} z^{3} + 42 y^{2} z^{5} + 2 z^{7}

= 14 y^{6} z + 70 y^{4} z^{3} + 42 y^{2} z^{5} + 2 z^{7}

2 \times 1 0^{- 3}

2 ln (e^{5})

2^{l o g_{2} (9)}

23 + 227

2 \cdot π \cdot 6

What is expand (y+z)^7-(y-z)^7 ?
The solution to expand (y+z)^7-(y-z)^7 is 14y^6z+70y^4z^3+42y^2z^5+2z^7